Methods for reducing polarization aberration in optical systems

ABSTRACT

An optical system includes multiple cubic crystalline optical elements and one or more uniaxial birefringent elements in which the crystal lattices of the cubic crystalline optical elements are oriented with respect to each other to reduce the effects of intrinsic birefringence and produce a system with reduced retardance. The net retardance of the system is reduced by the cancellation of retardance contributions from the multiple cubic crystalline optical elements and the uniaxial birefringent element. The optical system may be used in a photolithography tool to pattern substrates such as semiconductor substrates and thereby produce semiconductor devices.

PRIORITY APPLICATION

This application is a divisional of U.S. application Ser. No 10/331,101,filed Dec. 26, 2002, now U.S. Pat. No. 7,072,102, issued Jul. 4, 2006,which claims priority to U.S. Provisional Application No. 60/432,688,filed Dec. 11, 2002, and U.S. Provisional Application No. 60/405,853,filed Aug. 22, 2002. The entire contents of these applications areincorporated herein by reference.

BACKGROUND OF THE INVENTION

1.Field of the Invention

The present invention relates to reducing aberration in optical systems.More particularly, the present invention relates to apparatus andmethods for reducing polarization aberrations in optical systems such aslithographic imaging systems comprising cubic crystalline opticalelements having intrinsic birefringence.

2.Description of the Related Art

In order to increase levels of device integration for integrated circuitand other semiconductor components, device features having smaller andsmaller dimensions are desired. In today's rapidly advancingsemiconductor manufacturing industry, the drive is to produce suchreduced device features in a reliable and repeatable manner.

Optical lithography systems are commonly used to form images of devicepatterns upon semiconductor substrates in the fabrication process. Theresolving power of such systems is proportional to the exposurewavelength; therefore, it is advantageous to use exposure wavelengthsthat are as short as possible. For sub-micron lithography, deepultraviolet light having a wavelength of 248 nanometers or shorter iscommonly used. Wavelengths of interest include 193 and 157 nanometers.

At ultraviolet or deep ultraviolet wavelengths, the choice of materialsused to form the lenses, windows, and other optical elements of thelithography system is significant. Such optical elements preferably aresubstantially optically transmissive at short wavelengths used in theselithography systems.

Calcium fluoride and other cubic crystalline materials such as bariumfluoride, lithium fluoride, and strontium fluoride, represent some ofthe materials being developed for use as optical elements for 157nanometer lithography, for example. These single crystal fluoridematerials have a desirably high transmittance compared to ordinaryoptical glass and can be produced with good homogeneity.

Accordingly, such cubic crystalline materials are useful as opticalelements in short wavelength optical systems including but not limitedto wafer steppers and other projection printers used to produce smallfeatures on substrates such as semiconductor wafers and other substratesused in the semiconductor manufacturing industry. In particular, calciumfluoride finds particular advantage in that it is an easily obtainedcubic crystalline material and large high purity single crystals can begrown. These crystals, however, are expensive, and certain orientations,such as the <100> and <110>; crystallographic orientations are moreexpensive than others, like the <111>; crystal orientation.

A primary concern regarding the use of cubic crystalline materials foroptical elements in deep ultraviolet lithography systems is anisotropyof refractive index inherent in cubic crystalline materials; this effectis referred to as “intrinsic birefringence.” For light propagatingthrough a birefringent material, the refractive index varies as afunction of polarization and orientation of the material with respect tothe propagation direction and the polarization. Accordingly, differentpolarization components propagate at different phase velocities andundergo different phase shifts upon passing through an optical elementcomprising birefringent material.

When used for construction of elements of an optical system, thebirefringent properties of these cubic crystalline materials may producewavefront aberrations that significantly degrade image resolution andintroduce field distortion. These aberrations are particularlychallenging for optical instruments employed in photolithography intoday's semiconductor manufacturing industry where high resolution andtight overlay requirements are demanded by an emphasis on increasedlevels of integration and reduced feature sizes.

It has been recently reported [J. Burnett, Z. H. Levine, and E. Shipley,“Intrinsic Birefringence in 157 nm materials,” Proc. 2^(nd) Intl. Symp.on 157 nm Lithography, Austin, Intl. SEMATECH, ed. R. Harbison, 2001]that cubic crystalline materials such as calcium fluoride, exhibitintrinsic birefringence that scales as the inverse of the square of thewavelength of light used in the optical system. The magnitude of thisbirefringence becomes especially significant when the optical wavelengthis decreased below 250 nanometers and particularly as it approaches 100nanometers. Of particular interest is the effect of intrinsicbirefringence at the wavelength of 157 nanometers (nm), the wavelengthof light produced by an F₂ excimer laser, which is favored in thesemiconductor manufacturing industry. Strong intrinsic birefringence atthis wavelength has the unfortunate effect of producing wavefrontaberrations that can significantly degrade image resolution andintroduce distortion of the image field, particularly for sub-micronprojection lithography in semiconductor manufacturing.

Thus, there is a need to reduce these wavefront aberrations caused byintrinsic birefringence, which can degrade image resolution and causeimage field distortion. Such correction is particularly desirable inprojection lithography systems comprising cubic crystalline opticalelements using light having wavelengths in the deep ultraviolet range.

SUMMARY OF THE INVENTION

One aspect of the invention comprises a method of optically imaging,comprising:

propagating light through a plurality of cubic crystal elementspossessing intrinsic birefringence that produce first retardanceaberrations; and

propagating said light through one or more optical elements comprising auniaxial birefringent medium thereby introducing second retardanceaberrations substantially identical in magnitude and substantiallyconjugate in shape to said first retardance aberrations so as tosubstantially offset said first retardance aberrations.

Another aspect of the invention comprises a method of reducing theretardance caused by intrinsic birefringence in an optical systemcomprising a plurality of [111] cubic crystalline optical elements withrespective [111] crystal axes aligned along an optical axis, said methodcomprising:

clocking at least one said [111] cubic crystalline optical element toprovide a more circularly symmetric retardance pattern over a pupilcentered about said optical axis at least for on-axis field points; and

introducing one or more uniaxial birefringent elements comprising mediahaving a single birefringence axis into said optical system, said one ormore uniaxial birefringent elements having a substantially circularlysymmetric retardance pattern associated therewith that is distributedover said pupil centered about said optical axis at least for on-axisfield points, wherein said retardance pattern corresponding to saidplurality of [111] cubic crystal optical elements and said retardancepattern corresponding to said one or more uniaxial birefringent elementsare opposite such that retardance introduced into an optical beamtransmitted through said plurality of [111] cubic crystalline elementsis substantially offset by retardance introduced into said optical beamupon transmitting said beam through said one or more uniaxialbirefringent optical elements.

Still another aspect of the invention comprises an optical methodcomprising:

-   -   propagating a beam of light having first and second orthogonal        polarization components through first optics comprising a        plurality of optical elements disposed along an optical axis,        said first optics having radial and tangential eigenpolarization        states that form a circularly symmetric pattern around said        optical axis, said radial and tangential eigenpolarization        states being phased delayed with respect to each other so as to        introduce phase delay between said first and second orthogonal        polarization components in said beam of light; and    -   substantially reducing said phase delay between said first and        second orthogonal polarization components in said beam of light        by propagating said light through second optics disposed along        said optical axis, said second optics having radial and        tangential eigenpolarization states that form a circularly        symmetric pattern around said optical axis, said radial and        tangential eigenpolarization states in said second optics being        phased delayed with respect to each other opposite said phase        delay between said radial and tangential eigenpolarization        states of said first optics section.

Yet another aspect of the invention comprises an optical methodcomprising:

-   -   propagating a beam of light having first and second orthogonal        polarization components through first optics comprising a        plurality of optical elements disposed along an optical axis,        said first optics having radial and tangential eigenpolarization        states that form a circularly symmetric pattern around said        optical axis, said radial and tangential eigenpolarization        states being phased delayed with respect to each other so as to        introduce phase delay between said first and second orthogonal        polarization components in said beam of light; and    -   substantially reducing said phase delay between said first and        second orthogonal polarization components in said beam of light        by propagating said light through second optics disposed along        said optical axis, said second optics having radial and        tangential eigenpolarization states that form a circularly        symmetric pattern around said optical axis, said radial and        tangential eigenpolarization states in said second optics being        phased delayed with respect to each other opposite said phase        delay between said radial and tangential eigenpolarization        states of said first optics section.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention and advantagesthereof may be acquired by referring to the following description, takenin conjunction with the accompanying drawings in which like referencenumbers indicate like features and wherein:

FIG. 1 is a cross-sectional view of a projection optics for an exemplarylithography system comprising twenty-one optical elements (eighteentransmissive and three reflective);

FIG. 2 is a schematic diagram of an exemplary lithography systemincluding a condenser lens and projection optics;

FIG. 3A is a graphical representation of variation of birefringence axisorientation with respect to a cubic crystal lattice;

FIG. 3B is a graphical representation of variation of birefringencemagnitude with respect to a cubic crystal lattice;

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice;

FIG. 5A is a graphical illustration of retardance magnitude andretardance axis orientation in angular space for a cubic crystallinematerial with respect to the [110] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5B is a graphical illustration of retardance magnitude andretardance axis orientation in angular space for a cubic crystallinematerial with respect to the [100] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5C is a graphical illustration of retardance magnitude andretardance axis orientation in angular space for a cubic crystallinematerial with respect to the [111] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIGS. 6A and 6B illustrate the application of stress to an opticalelement to produce a uniaxial birefringent structure having a singlebirefringence axis substantially parallel to the optical axis of theelement;

FIG. 7 is a graphical illustration showing the net retardance for anexemplary stressed element such as shown in FIGS. 6A and 6B across theexit pupil for an on-axis field point, wherein the optical elementcomprises cubic crystalline calcium fluoride having with its [100]crystal axis aligned along optical axis;

FIG. 8 is a schematic illustration of a form birefringent elementcomprising a multilayer coating;

FIG. 9 is a graphical illustration showing the net retardance for anexemplary form birefringent element such as shown in FIGS. 8 across theexit pupil for an on-axis field point, wherein the form birefringentelement has a single birefringence axis parallel to the optical axis;

FIGS. 10A and 10B are graphical illustrations showing the net retardanceat the exit pupil for an exemplary optical system such as shown in FIG.1 for on-axis and extreme field points, wherein the optical systemcomprises [111] cubic crystal calcium fluoride optical elements havingrespective crystal axes substantially identically aligned;

FIG. 11 is a cross-sectional view of a projection optics similar to thatshown in FIG. 1 further comprising a stress plate with uniaxialbirefrincence;

FIG. 12 is a graphical illustration showing the net retardance for anexemplary optical system such as shown in FIG. 11 across the exit pupilfor an off-axis field point;

FIG. 13 is a cross-sectional view of a projection optics similar to thatshown in FIG. 1 further comprising a form birefringent element;

FIG. 14 is a graphical illustration showing the net retardance for anexemplary optical system such as shown in FIG. 13 across the exit pupilfor an off-axis field point;

FIG. 15 is a schematic illustration of a form birefringent a multilayercoating that includes an impedance matching layer;

FIGS. 16A-16C are plots of transmittance (in percentage) versus angle ofincidence (in degrees) for a form birefringent multilayer on calciumfluoride, a form birefringent multilayer that includes impedancematching, and bare calcium fluoride;

FIGS. 17A and 17B are plots of phase shift (in degrees) versus angle ofincidence (in degrees) for a form birefringent multilayer on calciumfluoride without an impedance matching layer and with an impedancematching layer, respectively

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

It is well-known that cubic crystalline materials like calcium fluorideare favored in lithography systems such as the high performancephotolithographic tools used in the semiconductor manufacturingindustry. These crystalline materials are substantially transmissive toshort wavelength UV light, which provides for high optical resolution.It is also well-known, however, that these cubic crystalline materialsexhibit intrinsic birefringent, i.e., an inherent anisotropy inrefractive index.

Birefringence, or double-refraction, is a property of refractivematerials in which the index of refraction is anisotropic, that is, theindex of refraction and thus the phase velocity is different fordifferent polarizations. For light propagating through a birefringentmaterial, the refractive index varies as a function of polarization andorientation of the material with respect to the polarization and thusthe propagation direction. Unpolarized light propagating through abirefringent material will generally separate into two beams withorthogonal polarization states. These beams may be referred to aseigenpolarization states or eigenpolarizations. The two beams propagatethrough the material with a different phase velocity. As the lightpasses through a unit length of the birefringent material, thedifference in phase velocity for the two ray paths will produce a phasedifference between the polarizations, which is conventionally referredto as retardance. These two states having different phase velocities maybe referred to as the slow and fast eigenpolarization states.

Birefringence is a unitless quantity, although it is common practice inthe lithography community to express it in units of nanometer percentimeter (nm/cm). Birefringence is a material property, whileretardance is an optical delay between polarization states. Theretardance for a given ray through an optical system may be expressed innanometers (nm), or it may be expressed in terms of number of waves of aparticular wavelength.

In uniaxial crystals, such as magnesium fluoride or crystal quartz, thedirection through the birefringent material in which the two orthogonalpolarizations travel with the same velocity is referred to as thecrystal axis. The term optic axis is commonly used interchangeably withcrystal axis when dealing with single crystals. In systems of lenselements, the term optical axis usually refers to the symmetry axis ofthe lens system. To avoid confusion, the term optical axis will be usedhereinafter only to refer to the symmetry axis in a lens system.

In one simplified case, useful for conceptualizing certain properties ofuniaxial crystals, the two orthogonal polarizations are linearpolarization components that are directed vertically and horizontally ina plane perpendicular to the direction of propagation of the ray. Inthis particular example, as well as in general, the two orthogonalpolarizations will travel with different velocities for directionsthrough the material other than the crystal axis. For a given incidentray upon a birefringent medium, the two refracted rays associated withthe two orthogonal polarization states are commonly described as theordinary and extraordinary rays. The ordinary ray is polarizedperpendicular to the crystal axis and refracts according to Snell's Law,and the extraordinary ray is polarized perpendicular to the ordinary rayand refracts at an angle that depends on the direction of the crystalaxis relative to the incident ray and the amount of birefringence. Inuniaxial crystals, the ordinary ray experiences the same index ofrefraction regardless of propagation direction of the ray, as bydefinition the ordinary ray is polarized perpendicular to the crystalaxis. The polarization of the extraordinary ray is not alwaysperpendicular to the crystal axis. Accordingly, the refractive index ofthe extraordinary ray depends on the propagation direction, i.e., angle,of the ray with respect to the crystal axis. For uniaxial crystals, theindex of refraction of the extraordinary ray is the same for all raysthat propagate at the same angle. The result is symmetry about thecrystal axis as will be illustrated more fully below. For example, thedifference between the ordinary and extraordinary index is constant forrays propagating at the same angle with respect to the crystal axis.Similarly, the retardance is rotationally symmetric about the crystalaxis. As is well known, uniaxial crystals are commonly used for opticalcomponents such as retardation plates and polarizers.

In contrast, however, the index of refraction is generally not the samefor all rays that propagate at the same angle. As a result, theretardance experienced is not rotationally symmetric about a singleline. Cubic crystals have been shown to have both a retardance axisorientation and magnitude that vary depending on the propagationdirection of the light with respect to the orientation of the crystallattice. However, in contrast with a uniaxial crystal that has twopropagation directions where the retardance is a maximum, i.e., the twoopposite directions along the optic or crystal axis, cubic crystals mayhave a maximum birefringence along twelve different propagationdirections through the cubic crystal.

In addition to retardance, which is the difference in the index ofrefraction seen by the two eigenpolarizations, in cubic crystals theaverage index of refraction also vanes as a function of angle ofincidence, which produces polarization independent phase errors.

Optical elements constructed from a cubic crystalline material, maycause a wavefront to be retarded as a result of the intrinsicbirefringence of the optical element. Moreover, the retardance magnitudeand orientation at a given point on the wavefront may vary, because thelocal propagation angle with respect to the material or the optical pathlength varies across the pupil. Such variations in retardance across thewavefront may be referred to as “retardance aberrations.” Retardanceaberrations split a uniformly polarized or unpolarized wavefront intotwo wavefronts with orthogonal polarizations. Again, these orthogonalwavefronts correspond to the eigenpolarization states. Each of theorthogonal wavefronts will experience a different refractive index,resulting in different wavefront aberrations.

Optical elements comprising cubic crystalline material thereforeintroduce additional aberrations that are correlated with polarization.These aberrations are generally referred to herein as polarizationaberrations and include the retardance aberrations described above whichresult from intrinsic birefringence in cubic crystalline materials.Additionally, these polarization aberrations include diattenuation, thevariation in optical transmission with polarization.

In cubic crystalline material, these polarization aberrations aresignificant enough to affect image quality in optical systems such asphotolithography system used in semiconductor fabrication processing.Accordingly, methods and apparatus for reducing these aberrations havesignificant value.

For ease of description, the cubic crystalline materials have crystalaxis directions and planes described herein using the well-known Millerindices, which are integers with no common factors and that areinversely proportional to the intercepts of the crystal planes long thecrystal axes. Lattice planes are given by the Miller indices inparentheses, e.g. (100), and axis directions in the direct lattice aregiven in square brackets, e.g. [111]. The crystal lattice direction,e.g. [111], may also be referred to as the [111] crystal axis of thematerial or optical element. The (100), (010), and (001) planes areequivalent in a cubic crystal and are collectively referred to as the{100} planes.

As discussed above, for cubic crystalline materials, the magnitude ofretardance depends on the direction of light propagation through thecrystal with respect to the orientation of the crystal axes and theoptical path length within the birefringent medium. For example, lightpropagating through an exemplary cubic crystalline optical element alongthe [110] crystal axis experiences the maximum retardance, while lightpropagating along the [100] crystal axis experiences no retardance.

Unfortunately, when constructing optical systems from cubic crystallinematerials such as calcium fluoride, the cost of the optical elementscontributes significantly to the total cost of these optical systems. Inparticular, the expense of the materials used to fabricate therefractive optical elements drives up the cost. Moreover, opticalelements comprising calcium fluoride having an optical axis directedalong the [100] crystalline directions, which has the least retardance,is the most expensive to fabricate. Blanks for creating refractiveelements having an optical axis corresponding to [110] are alsoexpensive. In contrast, calcium fluoride grown (or cleaved) in the [111]direction is significantly less expensive to fabricate. However, asdescribed above, optical elements having an optical axis generallycoinciding with the [111] direction of the crystalline material althoughleast expensive, possess intrinsic birefringence which introduceswavefront aberrations that degrade performance of optical systems suchas image quality and resolution. Although both [100] and [111] opticalelements have zero retardance along their respective optical axes, for[100] optical elements, the retardance increases more slowly for raysfurther and further off-axis.

FIG. 1 is a schematic illustration of a projection optics section 100 ofan exemplary lithography system. The optical system 100 shown in FIG. 1is substantially similar to the optical system shown and described inEuropean Patent Application No. 1 115 019 A2 by D. Shafer et al. Thisexemplary optical system 100 is a large format catadioptric projectionlens having an NA of 0.8,designed for a wavelength of 157.63 nm andwhich provides a 5× reduction. Such an optical system 100 is intended tobe exemplary only and other optical imaging systems and non-imagingsystems may be used in other embodiments. The optical system 100,however, may be the projection optics section of a lithography tool inone preferred embodiment. As shown in FIG. 1, the projection lens 100 isdisposed between a reticle 102 and a substrate 104. The reticle 102 maybe considered to correspond to the object field with the substrate 104in the image field of the projection lens 100.

The optical system 100 shown is a lens system, commonly referred tocollectively as a “lens,” comprising a plurality of, i.e., twenty-one,individual optical elements A1-A21, an optical axis 106, and aperturestop (AS) 10. The reticle 102 includes a mask pattern, which is to beprojected onto a surface 110 of the substrate 104. Substrate 104 may,for example, be a semiconductor wafer used in the semiconductormanufacturing industry, and surface 110 may be coated with aphotosensitive material, such as a photoresist commonly used in thesemiconductor manufacturing industry. Other substrates may be usedaccording to other embodiments and applications. Reticle 102 may be aphotomask suitable for various microlithography tools. Generallyspeaking, the reticle or photomask, hereinafter referred to collectivelyas reticle 102, includes a pattern in the object field. The pattern mayfor example be clear and opaque sections, gray scale sections, clearsections with different phase shifts, or a combination of the above.Light is propagated through the pattern, and the pattern is projectedthrough the lens, system 100 and onto surface 110 of substrate 104. Thepattern projected from the reticle 102 onto substrate surface 110 may beuniformly reduced in size to various degrees such as 5:1, 4:1 or others.The optical system 100 may have a numerical aperture, NA, of 0.8, but isnot so limited. Systems having other numerical apertures, such as forexample between about 0.60 to 0.90 or beyond this range are conceivable.

The arrangement of the plurality of elements A1-A21, is intended to beexemplary only and various other arrangements of individual lenselements having various shapes and sizes and comprising differentmaterials may be used according to other exemplary embodiments. Theelement thicknesses, spacings, radii of curvature, asphericcoefficients, and the like, are considered to be the lens prescription.This lens prescription is not limited and will vary with application,performance requirements, cost, and other design considerations.

The optical system 100 shown in FIG. 1, includes seventeen lens elementsA1, A3-A5, A8-A20 as well as a window A21. These eighteen opticalelements A1, A 3-A5, A8-A21 are substantially optically transmissive atthe wavelength of operation, i.e., for example to wavelengths of 157nanometers. The optical system 100 further includes three reflectiveoptical elements A2, A6, and A7, one of which is curved and has power(A6). More or less optical elements may be included in other designs. Inother embodiments, these elements may be powered or unpowered,refractive, reflective, or diffractive and may be coated or uncoated.The individual optical elements, A1-A21, are arranged along the commonoptical axis 106 that extends through the lens 100.

In the case where the optical system 100 comprises a plurality ofindividual lens elements A1, A3-A5, A8-A20, or other opticallytransmissive components, preferably one or more comprises cubiccrystalline material. Cubic crystalline materials such as for examplesingle crystal fluoride materials like strontium fluoride, bariumfluoride, lithium fluoride, and calcium fluoride may be used. Asdiscussed above, calcium fluoride is one preferred material foroperation with ultraviolet (UV) light. In an exemplary embodiment, mostor even all of the cubic crystalline optical elements are formed of thesame cubic crystalline material. This cubic crystalline material mayalso have the same crystallographic orientation with respect to theoptical axis of the lens 100. In one preferred embodiment, a majority ofthe lens elements comprise cubic crystal such as cubic crystal calciumfluoride having a <111>; crystal axis substantially aligned with theoptical axis, as these crystals are less expensive than othercrystallographic directions. In one embodiment, all of the lens orpowered optical elements comprise <111> crystal. Non-poweredtransmissive optical elements, for example, windows A21, if any, mayalso comprise <111> crystal. The lens 100 may also include substantiallytransmissive optical elements, which are formed of non-cubic crystallinematerial such as low-OH fused silica, also known as dry fused silica.

FIG. 2 is a schematic illustration showing the optical system 100functioning as the projection optics section within a larger lithographytool 50. FIG. 2 shows an optical source 112 and the substrate 104. Thereticle 102 is disposed between condenser optics 114 and projectionoptics 100. The optical field of reticle 102 may be of variousdimensions. Each of the projection optics 100 and condenser optics 114may include an aperture stop and a plurality of lens elements, windows,and/or other refractive, reflective, catadioptric, and diffractivemembers. The lithography tool 50 shown in FIG. 2 is aligned along theoptical axis 106. This lithography tool 50 may be a wafer stepper,projection printer, or other photolithography or microlithography toolused in the semiconductor industry. The lithography tool 50 may likewisebe a scanning optical system, a step-and-repeat optical system or othermicrolithography or projection optics system. In a scanning-type opticalsystem, a pattern on reticle 102 is projected and scanned ontocorresponding sections of surface 110 of substrate 104. In astep-and-repeat optical system, such as a conventional wafer stepper,the pattern on reticle 102, is projected onto multiple differentportions of surface 110 in a plurality of discrete operations. In eithercase, the reticle pattern includes various field points which areprojected onto surface 110 simultaneously.

The pattern printed on reticle 102 may be used to create a circuitpattern on surface 110 for an integrated circuit device being fabricatedon the substrate 104. The pattern may be projected onto a photosensitivematerial formed on the surface 110 to create an exposure pattern. Theexposure pattern may be developed using conventional means, to produce aphoto-pattern in the photosensitive material. The photo- pattern may betranslated into the substrate 104 by etching or other method. Aplurality of layers of materials can be deposited thereon. The surface110 may be one of the layers and the photo-pattern formed on the layer.Etching or other techniques may be used to translate the photo-patterninto the layer. Similarly-formed photo-patterns may be used to enablespatially selective doping using known methods such as ion implantation.In this manner, multiple photolithographic operations, may be used toform various patterns in various layers to create a completedsemiconductor device such as an integrated circuit. An advantage of theinnovative techniques described herein is that images formed on thesubstrate 104 have sufficiently low aberration to enable preciselydimensioned and aligned device features to be created having reducedsizes.

In one exemplary scanning optical system, the optical field of thereticle 102 which is projected and scanned onto the substrate surface110 has a height of few centimeters and a width of a few millimeters.Other field dimensions may be used which are suitable for the specificapplications and may depend on the type of lithography tool in which theprojection optics are included. Similarly, the format at the image planewhere the wafer is located may vary as well.

The optical source 112 produces light that is subsequently shaped andconditioned by condenser lens 114. The optical wavelength of source 112may vary, and may be no greater than 248 nanometers in some cases. Inone preferred embodiment, light having a wavelength of about 157nanometers may be used. The optical source 112 may produce linearlypolarized light. One optical source that produces linearly polarizedlight is an excimer laser. In other embodiments, the optical source 112may produce light having other polarizations or which is substantiallynon-polarized. A KrF excimer laser operating at about 248 nm, an ArFexcimer laser operating at about 193 nm, or a F₂ excimer laser operatingat about 157 nm, are examples of various optical sources 112.

The light produced by the optical source 112 is shaped and conditionedby the condenser lens 114 and propagated through the reticle 102 and theprojection optics 100 to project an image of the reticle 102 orphotomask onto the substrate 110. This light may be described as a lightbeam comprised of a plurality of rays. In accordance with convention,the marginal ray is the ray from the point on the object field 102intersecting the optical axis 106, to the edge of the aperture 108 andalso intersects the axis 106 at the image field 104. The chief ray isthe ray from a given field point that passes through the center of theaperture stop 108 and system pupils in the optical system 100. For anobject field point located where the optical axis 106 intersects thereticle 102, the chief ray travels along the optical axis 106. Lightrays emanating from an individual object field point on the reticle orphotomask 102 correspond to a wavefront that is propagated through theprojection lens 100 and are ideally focused down to a correspondingimage field point at the substrate 104. The full image field istherefore generated by a plurality image field points with correspondingwavefronts associated therewith.

As described above, these wavefronts may be aberrated as a result ofretardance, which has magnitude and orientation that varies withdirection in cubic crystalline materials, as a result of intrinsicbirefringence. FIG. 3A is a three-dimensional vector plot showing thespatial variation in retardance axis orientation within a materialhaving a cubic crystalline lattice. The cubic crystalline lattice may bethat of calcium fluoride, for example. The crystal axis directions shownin FIG. 3A as well as in FIG. 3B are described using Miller indices.FIG. 3B is a three-dimensional plot corresponding to a quadrant of thevector plot shown in FIG. 3A, and depicts the corresponding magnitude ofthe retardance from a cubic crystal. It can be seen that the localizedmagnitude and axis of the retardance vary spatially throughout thecrystal in a known fashion. It can also be seen that, depending on thedirection along which light travels through such a cubic crystallinematerial, the retardance magnitude and the orientation of the retardanceaxis relative to the direction of propagation will vary. FIG. 3Brepresents an octant of the crystal lattice; the extension of thisdiagram to all possible directions through the crystal gives twelvedirections with maximum retardance, herein referred to as retardancelobes.

The crystalline material can therefore be advantageously cut along agiven plane and arranged such that light normal to that plane travelsalong a chosen axis direction. For example, light traveling along the[100] crystal axis 130 (i.e. along the [100] crystal lattice direction),which is oriented normal to the (100) crystal lattice plane 132, sees afixed and deterministic localized retardance. The retardance magnitudeand retardance axis direction encountered by a given ray thereforevaries as a function of the direction along which the light ray travelsthrough the crystal.

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice. Thecubic crystalline lattice may be that of calcium fluoride, for example.FIG. 4 includes the peak retardance directions along the [101], [110],and [011] lattice directions, indicated by lines 142, 144, and 146,respectively. Line 140 represents the [111] crystal axis direction,which corresponds to a direction through the crystal with no retardance.

FIGS. 5A, 5B, and 5C are schematic representations of the variations inretardance magnitude per unit length in the crystal and retardance axisorientation in angular space for optical axis 106 orientations in the[110], [100], and [111] lattice directions, respectively, for the cubiccrystalline lattice structure shown in FIG. 4. The total retardancethrough a crystal is the product of the retardance per unit length for agiven ray and the path length. The center of the plot represents theretardance encountered by a ray traveling along the indicated crystalaxis and normal to the plane of the illustration. Retardance depicted atincreased radial distance from the center represents the retardance forrays at increased angles of propagation with respect to the optical axis106. These plots, therefore can be used to visualize the retardanceencountered from a plurality of rays emanating from a point, e.g. on theoptical axis 106 through a lens element comprising for example [111]material. The ray through the optical axis 106 propagates in the [111]direction through the center of the lens element and encounters aretardance with magnitude and orientation specified at the center of theplot. A ray emanating from the point on the axis but angled willexperience retardance specified by the direction indicated on theseplots. In each of FIGS. 5A-5C, the localized retardance axis isindicated by the direction of lines plotted on a square grid, and themagnitude is indicated by the relative length of the lines.

The variation of retardance magnitude in FIGS. 5A-5C is characterized byseveral lobes, also referred to as nodes, distributed azimuthally inwhich the retardance is maximized. Each of FIGS. 5A-5C shows peakretardance lobes with respect to the various crystal axis directions inthe cubic crystalline lattice shown in FIG. 4. The spatial orientationof the cubic crystalline lattice is indicated by the other relatedcrystalline lattice directions indicated by the arrows. For example, inFIG. 5A in which the center represents retardance encountered by a raytraveling along the [110] crystal axis, a ray traveling along the [101]lattice direction is at a greater angle with respect to the [110]crystal axis than a ray traveling along the [111] lattice direction;these ray angles are at 60° and 35.3°, respectively. This is indicatedby the [101] arrowhead positioned at a greater radial distance fromcenter than the [111] arrowhead. The relative azimuthal directions ofthe indicated [100], [101], and [111] lattice directions are as shown inFIG. 4. This description applies to FIGS. 5B and 5C as well.

Referring to FIGS. 5A-5C, in each case, the indicated crystal axis isthe direction normal to the plane of the paper and at the center of eachof the respective figures. FIG. 5A shows retardance with respect to the[110] lattice direction, including peak retardance lobes 150A, 150B,150C and 150D, each which forms an angle of 60° with respect to the[110] crystal axis direction. [110] retardance also includes a centralretardance node. FIG. 5B shows retardance with respect to the [100]lattice direction, including peak retardance lobes 152A, 152B, 152C and152D each of which forms a 45° angle with respect to the [100] crystalaxis direction. Near the [100] axis, the retardance exhibits asubstantial circular symmetry with redardance axis oriented tangentiallyabout the [100] axis. There are also peaks along the diagonals at 90°not depicted. FIG. 5C shows retardance along the [111] latticedirection. The [111] cubic crystal exhibits a complex substantiallythree-fold retardance symmetry near the [111] axis. This retardance plotincludes peak retardance lobes 154A, 154B, and 154C, each of which formsan angle of 35.3° with respect to the [111] crystal lattice direction.

The crystal lattice and resulting retardance lobes with respect to thecrystal axes such as shown in FIGS. 5A-5C, correspond to the exemplarycase in which the cubic crystals are negative cubic crystals; that isthe ordinary refractive index is greater than the extraordinary index,so the birefringence, n_(e)−n_(o), is negative. Calcium fluoride is anexample of a negative cubic crystal. For positive cubic crystals, thepatterns would be substantially similar except the lines would be eachrotated by 90 degrees about their midpoints. It should be understoodthat other cubic crystalline optical elements such as barium fluoride,lithium fluoride, and strontium fluoride as well as other materialsmight be used to form optical elements. With respect to any cubiccrystalline material used, the variations in the retardance directionand magnitude can be measured, or calculated using computer modeling.Furthermore, the variations in retardance direction and magnitude of anoptical material may also be measured. Graphical representations of thevariations in retardance magnitude and axis orientations similar tothose shown in FIGS. 5A-5C can be similarly generated for each of theaforementioned cubic crystalline materials.

Referring again to FIG. 1, it can be understood that each of theindividual transmissive optical elements A1, A3-A5, and A8-A21 may beformed of the same cubic crystalline optical material such as calciumfluoride. Moreover, these optical elements may be formed from cubiccrystal having the same crystal orientation, e.g., [110], [100], or[111] cubic crystal, and may be arranged with substantially the samelattice orientation aligned with the optical axis 106. For example, theoptical elements A1, A3-A5, and A8-A21 may be oriented such that their[110] axes are aligned substantially parallel to the optical axis 106.In this case then, the net retardance of the lens system 100 will have aretardance that varies across the system exit pupil in a similar mannerto the angular retardance variation shown schematically in FIG. 5A.Similarly, if all the optical elements A1, A3-A5, and A8-A21 are alignedwith their [100] axes substantially parallel to the optical axis 106,then the net retardance of the lens system 100 will have a retardancethat varies across the system exit pupil in a similar manner to theangular retardance variation shown schematically in FIG. 5B.

Likewise, if all the optical elements A1, A 3-A5, and A8-A21 are alignedwith their [111] axes substantially parallel to the optical axis 106then the net retardance of the lens system 100 will have a retardancethat varies across the system exit pupil in a similar manner to theangular retardance variation depicted schematically in FIG. 5C.Accordingly, for a lens 100 comprising a plurality of [111] opticalelements with the respective [111] crystal directions alignedsubstantially along the optical axis 106, the retardance distributionincludes peak retardance lobes 154A, 154B, and 154C, each of which formsan angle of 35.3° with respect to the [111] crystal lattice direction.Also as illustrated in FIG. 5C, a large portion of the local retardanceaxes within these lobes 154A, 154B, and 154C are oriented substantiallyradially away from the [111] axis. An inset to FIGS. 5C depicts anexemplary radial direction represented by a vector {right arrow over(R)} extending from a center point, C. This centerpoint, C, iscoincident with the optical axis 106, (i.e. the Z axis) which is shownin the inset at the intersection of X and Y axes. [0080] Located betweenthese retardance lobes 154A, 154B, 154C are sections 164A, 164 B, 164Ccorresponding to generally lower retardance than within the lobes. Asshown, the retardance axes in these sections 164A, 164B, 164C, are notsubstantially radially directed, i.e. oriented in a radial directionaway from the optical axis 106, as are the retardance axes found in thelobes 154A, 154B, and 154C. Accordingly, for many lenses 100 comprisinga plurality of [111] optical elements with the respective [111] crystaldirections aligned substantially identically along the optical axis, theretardance oscillates between high and low values in the tangentialdirection, T, that is along circular paths 170 centered about theoptical axis 106 as depicted in the inset. Thus, sampling thedistribution of rays passing through the exit pupil by sweepingazimuthally 360 degrees about the optical axis 106, which corresponds tothe angular direction φ;, the magnitude of the retardance may increaseand decrease. In addition, the retardance axes are oriented more in aradial direction in the peak regions 154A, 154B, and 154C, than in thesections 164A, 164 B, 164C between these lobes, especially at positionsin the pupil farther from the optical axis 106. For numerical aperturesgreater than about 0.5,this non-circularly symmetric effect will likelybe present. With smaller numerical apertures, and likewise smalleraperture stops and entrance and exit pupils, a level of circularsymmetry may be discernable. However, for large apertures and pupils andlarger bundles of rays, defined by larger f-numbers and numericalapertures, the observed pattern are more likely to be non-circularlysymmetric.

As described below, the local retardance axes in retardance patternspresented herein describe local retardance effects experienced by abundle of rays propagating though one or more optical elements. Thisbundle of rays may for example extend as a cone from a point on-axis.The expanse of this cone of rays may be defined by a solid angle ornumerical aperture. Different rays of light in this cone will beincident on the optical element or elements at different locations.Similarly, these different rays will also be located at differentpositions in the aperture or pupils associated with the optical elementor plurality of optical elements. Moreover, these different rays oflight will be incident on the optical element(s) at different verticaland horizontal angles and have different path lengths through theoptical elements. The variation in vertical and horizontal angle andoptical path length results in different retardance which may becharacterized by the retardance patterns or retardance distributionsmapped across a selected region such as a reference plane or referencesphere. The retardance pattern may, for example, be mapped at the exitpupil. These local retardance axes are therefore constructs used tocharacterize the retardance encountered by a ray of light passingthrough a specific location in the pupil. Retardance patterns correspondto distributions of the retardance experienced by a plurality of rays oflight at, for example, a reference sphere at the pupil. Anotherconstruct useful for characterizing the retardance of an optical system100 are the eigenpolarization states as discussed more fully below.

The actual retardance experienced by this bundle of rays propagatingthrough the optical system 100 will depend on the optical properties ofthe elements as determined, for example, by their shapes, thicknesses,and separations, etc. In addition, the retardance pattern may beaffected by the field angle. In the discussion above with respect toFIG. 5C, wherein the optical axis 106 is aligned with the [111]direction, the bundle of rays was assumed to pass through on-axis imageand object points.

Other configurations, however, are possible. In various preferredembodiments described herein, one or more of the optical elements A 1,A3-A5, and A8-A21 are rotated about the optical axis 106 to alter theretardance distribution. The process of generally rotating one or moreof the transmissive optical elements A1, A3-A5, and A 8-A21 about theoptical axis 106 is referred to as clocking.

In various preferred embodiments described herein, [111] cubic crystaloptical elements are clocked to provide more uniform retardancecharacteristics for rays propagating through the lens system 100.Preferably, this azimuthal rotation in the ±φ direction, causes theregions 154A, 154B, 154C and 164A, 164B, and 164C associated with theoptical elements A1, A3-A5, and A8-A21 to overlap and merge, forming amore homogeneous retardance distribution. For example, one or more ofthe optical elements A 1, A3-A5, and A8-A21 may be rotated clockwise orcounter-clockwise such that the lobes 154A, 154B, 154C associated withthe rotated elements are superimposed on the sections 164 A, 164B, 164Cbetween the lobes 154A, 154B, 154C of other elements. Contributions ofretardance at the lobes 154A, 154B, 154C can be introduced into sections164A, 164B, 164C between lobes. As a consequence, the differencesbetween the retardance lobes 154A, 154B, and 154C and sections 164A,164B, 164C there between is reduced. The result in a more uniform, lessvaried, distribution of retardance, both in amplitude and orientation.Accordingly, the three retardance peaks 154A, 154B, and 154C shown inFIG. 5C are not as pronounced or are more preferably substantiallyremoved. Variation along concentric circular paths about the optic axis106 is preferably reduced. In addition to decreasing change in magnitudeof retardance, the retardance axes are preferably more radially directedas a result of the rotations. The radially directed retardance axis inthe lobes 154A, 154B, 154C is preferably introduced into the sectionsbetween the lobes 164A, 164B, and 164C as the optical elements A1,A3-A5, and A8-A21 are rotated to provide overlap of the two types ofregions associated with separate optical elements. The result, ispreferably a lens system 100 having a retardance pattern, for example,in the exit pupil plane, having substantially radially directedretardance axes extending in each radial direction about the opticalaxis 106.

The contributions of the retardance in the lobes 154A, 154B, 154Cpreferably provides a more circularly symmetric retardance patternhaving more radially oriented retardance axes as measured for example atthe exit pupil of a lens system 100 having numerical aperture of greaterthan about 0.5.More preferably, such retardance characteristics areachievable for lens systems 100 having numerical apertures of greaterthan about 0.75 or 0.85.Substantially circularly symmetric retardancepatterns at the exit pupil of the lens 100 at least for on-axis fieldsangles is preferably obtained for a first portion of the opticalelements in the lens 100.

In various embodiments, the retardance as measured at the pupil ispreferably about 50, 75,or 90 percent or more circularly symmetric aboutthe optical axis 106 for on-axis field points. Moreover, the circularsymmetry is such that the magnitude of retardance varies less than about30%, and more preferably less than about 20% or 10%, around a circularpath about the optical axis 106 for axial field points. In addition,more than about 70%, and more preferably greater than about 80 or 90%,of the local birefringene axes are substantially radially directedaround circular paths about the optical axis 106 in the used clearaperture at least for on-axis field points. The RMS retardance, however,resulting from this first portion, which preferably comprises [111]cubic crystalline optical elements, may be at least about 0.1 RMS wave,0.5 RMS waves or higher for numerical apertures of about 0.5 to 0.7 orhigher. Systems having lower retardance, for example, about 0.01 RMS orlower, are also possible. These values may apply to on-axis fields.

To reduce the net retardance of the lens 100, this first portion of thelens 100 is included together with a second portion comprising one ormore additional optical element that possesses a conjugate retardancepattern. The retardance of the second portion preferably at leastpartially cancels the retardance effects contributed by of the firstportion. The result is a reduced net retardance for the lens system 100.

Accordingly, the optical element or elements in the second portionpreferably impart a retardance as measured for example at the exit pupilthat is substantially circularly symmetric about the optical axis 106.These element(s) also preferably have retardance orthogonal to theradially directed retardance associated with the optical elements in thefirst portion of the lens system 100. The local retardance axes of thesecond portion of the lens 100 is therefore preferably tangentiallydirected, i.e., the local retardance axes preferably are substantiallyoriented along or tangential to concentric circular paths 170 centeredabout the optical axis 106. The tangential retardance of the secondportion is substantially orthogonal and opposite to the radialretardance pattern associated with the first portion of the lens 100 andthus the two at least partially cancel or offset each other.

Such compensation is preferably provided for optical systems 100 havingnumerical apertures greater than about a 0.5 numerical aperture. Thecontributions of the two portions to the net retardance, for example, atthe exit pupil is preferable substantially similar in magnitude yetopposite at least for on-axis field points so as to counter each other.Preferably, however, sufficient correction is provided for off-axisfield points as well.

In various preferred embodiments, the result is preferably wavefrontcorrection to a level of a few waves across the used clear aperture.Similarly, the retardance induced phase variation is between about 0.1to 1% or less across the beam.

A tangential retardance pattern suitable for use in the second portionof the lens 100 may be provided by a negative uniaxial crystal. Variousnegative uniaxial crystals have substantially circularly symmetricretardance distributions with local retardance axes directed radiallyfrom a central region. Such negative uniaxial crystals, however, aregenerally not substantially optically transmissive to UV wavelengthsequal to or less than for example about 248 nanometers, 193 nanometers,or 157 nanometers.

A tangential retardance pattern may also be provided by an opticalelement comprising a uniaxial birefringent medium, i.e., a medium havinga single real birefringent axis or optic axis associated with themedium. Preferably, this uniaxial birefringent axis is alignedsubstantially parallel to the optical axis 106 through the birefringentmedium such that a tangentially directed birefringent pattern inproduced.

The localized retardance axes distributed across the designatedreference plane or sphere such as a pupil or aperture are different fromthe physical birefringence axis associated with an opticallytransmissive material or medium. The local retardance axes describe theaffect of the physical birefringence axis or axes associated with thematerial or medium used to form the optical element or elements on aplurality of rays propagating through the optical system 100.Accordingly, the localized retardance axes and more broadly theretardance patterns vary with the numerical aperture and the fieldangle. Additionally, in contrast with the real birefringence axis oraxes of a birefringent material or medium, the localized retardanceaxes, may vary with the prescription of the lens 100. The birefringenceaxis or axes are material properties, which create variations inretardance, retardance patterns, or retardance distributions in a lenssystem.

The geometry of an optical element comprising a uniaxial medium with asingle birefringent axis aligned along the optical axis 106 produces atangential retardance pattern. Namely, this pattern includes localizedretardance axes, e.g., at the exit pupil, that are tangential toconcentric circular paths 170 centered about the optical axis 106.Accordingly, a uniaxial birefringent medium is a suitable candidate forthe optical element or elements in the second portion of the lens 100.Elements comprising this uniaxial birefringent medium in the secondportion may offset the birefringence and retardance associated with thefirst portion of the lens system 100 described above as having a radialdirected retardance distribution.

A uniaxial medium can be provided by applying stress to an opticalelement as shown in FIGS. 6A and 6B. Stressing a flat rectangular plate180 having front and rear planar surfaces on its four sides or edges 182can create a substantially uniform stress distribution across the planarsurfaces. Accordingly, the magnitude of the birefringence will besubstantially the same across the rectangular spatial extent of theplate 180. In FIG. 6A, the applied stress is represented by arrows 184.Preferably, the stress is applied uniformly, i.e., the amount of stressapplied in each direction is substantially the same, although otherdesigns are possible. The refractive index will vary as in a uniaxialcrystal, which has a single optic or birefringence axis. Similarly, thestressed flat rectangular plate 180 has a single birefringence axis andis a uniaxial birefringent medium. This single birefringence axis isnormal to the plane of the applied stress, i.e., in the Z directionwhich is normal to the X-Y plane. Accordingly, light propagating alongthe birefringence axis (i.e., parallel to the Z axis) is not retarded asthe electric fields are in the X-Y plane. In contrast, maximumretardance is produced for light propagating in the applied stressplane, i.e., in the X-Y plane, which has orthogonal polarizationsparallel and perpendicular to the birefringence axis.

The plate 180 itself may comprise, for example, cubic crystal such ascubic crystalline calcium fluoride as well as other materials. For auniaxial birefringent plate constructed by applying stress to a cubiccrystalline substrate, the stress birefringence coefficient is highestwhen the [100] crystal lattice direction is oriented along the systemoptical axis 106. The stress birefringence coefficient along the [100]direction is over 4 times larger than the coefficient along the [111]lattice direction (Alternative Materials Development (LITJ216) FinalReport—Stress Birefringence, Intrinsic Birefringence, and IndexProperties of 157 nm Refractive Materials, International SEMATECH, Feb.28, 2002,J. Burnett and R. Morton). Thus, for a given plate thickness,the stress necessary to create a given retardance may be substantiallyreduced or minimized by orienting the plate with its [100] crystallattice direction along the optical axis 106. The cubic crystallinestress elements are often used with the [100] orientation (see, e.g.,U.S. Pat. No. 6,201,634 issued to S. Sakuma).

A substantially uniform compressive hoop stress can also be applied tothe perimeter 192 of a circular window 190 such shown in FIG. 6B toproduce a circular uniaxial birefringent plate. Preferably, the resultis a substantially uniform magnitude of birefringence over the circulararea of the circular window. The applied stress is indicated by arrows194. For example, a clamp, brace, or other structure around theperimeter of the window 190 can be employed to apply compressive forces.

Oppositely directed force induces opposite birefringence. Compressiveand tensile forces applied to cubic crystalline calcium fluoride may beused to induce the appropriate type (i.e., negative or positive) ofbirefringence.

FIG. 7 is a graphical illustration showing the net retardance across theexit pupil for light propagating through a stressed flat plate 180, 190such as discussed above. In this simulation, retardance is computed fora cone of light rays through the stressed plate 180, 190 correspondingto a numerical aperture of 0.85.Also in this example, the plate 180, 190was assumed to have a thickness of 20 millimeter (mm) and to comprise[100] cubic crystalline calcium fluoride with its [100] crystal axisparallel with the optical axis 106.

In these plots, and the retardance pupil maps to follow, the retardanceis shown on a square grid across the system exit pupil for the opticalsystem of interest. As described above, the retardance will generallyvary across a wavefront propagating through a birefringent opticalsystem. Accordingly, the retardance will be different for differentlocations across a cross-section of the beam. The variation plotted inthese retardance maps is that across the exit pupil of the opticalsystem 100.

The retardance plots are described in general by ellipses, whichsometimes degenerate into lines that show one of the eigenpolarizationstates. As defined above, the eigenpolarization state is a polarizationstate that remains unchanged for a ray propagating through the opticalsystem at given pupil coordinates. The eigenpolarization in the plots isthe slow eigenpolarization state. The fast and the sloweigenpolarizations are orthogonal. The fast eigenpolarization statecorresponds to the eigenpolarization shown in the plot rotated 90° aboutits center. For example, if the local retardance, be it linear orelliptical, is in the vertical direction, the slow eigenpolarizationstate will be oriented in the vertical direction and the fasteigenpolarization state will be oriented horizontally. The direction ofthe ellipse is defined by its major axis; for a vertical ellipse, themajor axis is oriented in the vertical direction. We refer to the majoraxis as the retardance axis. The size of the ellipse or length of theline at a given pupil coordinate is proportional to the relativestrength of the retardance, i.e., the phase shift between the fast andslow eigenpolarizations.

Also, for the lenses and corresponding retardance maps, the coordinatesare defined using a right-handed coordinate system such that the systemoptical axis is in the +Z direction from the object towards the imageplane, the +Y axis is in the vertical direction, and the +X direction isorthogonal to the Y and Z axes. For the exit pupil retardance andwavefront maps, the plots describe variations over an exit pupilreference sphere for a given field point using a Cartesian coordinatesystem, where the X and Y coordinates are coordinates on the referencesphere projected onto a plane perpendicular to the chief ray.

The retardance distribution shown in FIG. 7 illustrates the effects ofstress induced birefringence on a beam of light. This beam can beconceptualized as a bundle of rays propagating through the stressedoptical element. More particularly, the retardance across the exit pupilfor a beam of light may be represented by a bundle of rays emanatingfrom an object point on the optical axis 106 through the plate 180, 190to a location on the image field ideally also located on the opticalaxis 106. This beam and corresponding bundle of rays fills a real orconstructive aperture associated with the plate 180, 190 and also fillsthe exit pupil. The retardance map in FIG. 7 displays the retardance forrays at each of the locations shown in the exit pupil. These retardanceplots thus represent the retardance sampled across this particular beamat the exit pupil.

The peak retardance computed in this example is approximately 0.48 wavesat a wavelength of 157.63 nanometers, and the RMS retardance valueacross the pupil is about 0.12 waves. The retardance was computed for anumerical aperture of about 0.85 and an on-axis field location.

The retardance plot was obtained by simulating the application of about1000 pounds of stress applied to a [100] calcium fluoride crystal. Themagnitude of the uniaxial stress birefringence scales linearly withstress. The stress-optical coefficient q₄₄ of 0.46×10⁻¹² Pa⁻¹ at awavelength of about 157 nanometers has been suggested by Burnett andMorton in Alternative Materials Development (LITJ216) Final Repor—StressBirefringence, Intrinsic Birefringence, and Index Properties of 157 nmRefractive Materials, International SEMATECH, Feb. 28, 2002) yielding auniaxial stress birefringence of about −1×10⁻⁵. Higher or lower appliedstresses may be possible, however, stresses of less than 1000 pounds arepreferred as calcium fluoride (CaF₂) may be considered relativelyfragile. The cubic crystal plate was also assumed to have a cubicintrinsic birefringence of about −1.1×10⁻⁶ for purposed of thesecalculations. The values employed in approximating retardance of thestressed plate 180, 190 are for illustrative purposes. Other values maybe used in other simulations as appropriate.

As illustrated, the stress-induced birefringence yields a tangentialretardance pattern, i.e., one wherein the orientation of the plottedeigenpolarization state is substantially tangential to concentriccircular paths 170 centered around the optical axis 106. The resultantpattern is also largely circularly symmetric, both in magnitude andorientation of the plotted eigenpolarization state. This patternresembles that produced by a negative uniaxial crystal having a singlebirefringence or optic axis and negative birefringence, since the stressbirefringence is much larger than the intrinsic birefringence (1×10⁻⁵versus −1.1×10⁻⁶). Accordingly, the application of stress is a way ofobtaining a birefringent structure that behaves substantially like amaterial having a single birefringence axis.

Stress can be applied to lenses to provide tangentially directedretardation patterns. The magnitude of the stress will not be uniformacross the aperture of the lens, rather, the stress will be larger orsmaller at different locations. Thus, the birefringence of the lens willnot be uniform and the lens material cannot be modeled as a homogenousuniaxial crystal. However, the variation in birefringence across thelens can provide additional degrees of freedom for the reduction of theretardance aberrations in lenses with intrinsic birefringent elements

Another technique for obtaining a uniaxial birefringent structure ormedium is through form birefringence. In various preferred embodiments,optical birefringence and more particularly form birefringence isobtained in a stack of alternating thin layers of material havingdifferent refractive indices. Specifically, when the layer thickness aremuch smaller than the wavelength of light propagating therethrough, theresultant birefringence of the aggregate structure is similar to that ofa uniaxial crystal having a single crystal axis substantially parallelto the optical axis. See, for example, Yeh and Gu, “Optics of LiquidCrystal Displays”, John Wiley & Sons., Inc. 1999,pp. 381-384.

An exemplary form birefringent structure comprising a stratified medium200 formed on a surface 201 of an optical element 202 is shown in FIG.8. This multilayer structure 200 is preferably substantially opticallytransmissive to the wavelength of operation, which may be ultraviolet.This multilayer structure 200 comprises alternating layers 204, 206 ofmaterials stacked on each other. The alternating layers 204, 206preferably have different indices of refraction.

Three pairs of such layers 204, 206 are depicted for illustrativepurposes, however, the multilayer structure 200 is not limited to thisnumber. More layers 204, 206 are preferred. The number of pairs oflayers 204, 206 may, for example be greater than 50 layers andpreferably are between about 100 to 2000.More or less layers are alsopossible. In addition, although the thickness of the alternating layers204 and 206 are shown as similar in FIG. 8, the design is not solimited. The layers 204 and 206 may have different thicknesses.

The alternating layers 204 and 206 may, for example, have indices ofrefraction n1, and n2, respectively. In the case where the thicknessesof these layers are less than the wavelength of light, interferenceeffects can be substantially avoided, and the multilayer structure 200will exhibit optical anisotropy. Moreover, the stack 200 behaves like anegative birefringent medium wherein ne, the index of refraction forextraordinary rays is less than, no, the index for ordinary rays (i.e.,ne<no). Preferably, the thicknesses of these two layers aresubstantially equal also, to maximize birefringence. The maximumbirefringence for the multilayer structure is given by the followingequation:

$\begin{matrix}{{\Delta\; n} = {{n_{e} - n_{o}} = \frac{- \left( {n_{2} - n_{1}} \right)^{2}}{\sqrt{2\left( {n_{1}^{2} + n_{2}^{2}} \right)}}}} & (1)\end{matrix}$when the layers have the same thickness.

In certain preferred embodiments for use with 157 nanometer light, one204 of the alternating layers may comprise lanthanum fluoride LaF₂ orgadolinium fluoride GdF₃ having an index of refraction of about 1.8while the other 206 of the alternating layers may comprise aluminumfluoride AlF₃ and magnesium fluoride MgF₂ having an index of refractionof about 1.47. The resultant birefringence is approximately −0.04. (Thisvalue is a maximum birefringence, i.e., the maximum difference betweenthe ordinary and extraordinary refractive indices. The maximum occurswhen light rays propagate in the plane of the layers. There isapproximately zero birefringence when the rays are normally incident onthe plurality of layer.) Other variations and other materials are alsosuitable.

The multilayer structure 200 may comprise a thin film coating formed onan optical element 202 such as but not limited to a powered refractiveelement, a plate or window, a reflector or a diffractive opticalelement. The thin film coating can be on a flat or curved surface. Suchcurvature may affect the retardance distribution and provides anadditional degree of freedom for controlling retardance. The localbirefringence axis will be along the surface normal. Additionally,forming the thin film coating on curved surface allows integration ofthe uniaxial birefringent medium with powered optical elements.Conventional thin film deposition and/or fabrication techniques may beemployed to create such a structure 200, however, other methodsincluding those not yet developed are considered possible.

As discussed above, the multilayer structure 200 behaves like a uniaxialcrystal having a local birefringent or crystal axis normal to the stackof layers, i.e., in the Z direction illustrated in FIG. 8. Thebirefringent axis, which is normal to the interfaces between thealternating layers 204, 206 is preferably parallel to the optical axis106 of the optical element 202 and the optical system 100 in which it isincluded. In addition, the magnitude of the birefringence is preferablyuniform across the resultant form birefringent optical element. Forexample, for a coating on a circular plate, the magnitude of thebirefringence is preferably substantially constant across the circularspatial extent of the plate. The effect of the birefringence will bedifferent at different locations across the plate, if the angle of lightincident on the plate is dissimilar at these different locations asshown by the retardance distributions.

FIG. 9 is a graphical illustration showing the net retardance across theexit pupil for light propagating through a form birefringence mediumsuch as the thin film coating structure 200 as shown in FIG. 8. In thisexample, the thin film coating has a thickness of 1 micron (μm) and hasa form birefringence of about −0.04. Retardance is computed for a coneof light rays through the form birefringence coating corresponding to anumerical aperture of about 0.85.The cone is normally disposed withrespect to the coating.

As illustrated, the form birefringence multilayer thin film structure200 yields a tangential retardance pattern, i.e., one wherein theorientation of the plotted eigenpolarization state is substantiallytangential to concentric circular paths 170 centered around the opticalaxis 106. The resultant pattern is also largely circularly symmetric,both in magnitude and orientation of the plotted eigenpolarizationstate. This pattern resembles that produced by a negative uniaxialcrystal having a single birefringence axis and negative birefringence.Accordingly, the deposition of a form birefringent coating is a way ofobtaining a uniaxial birefringent structure that behaves like a uniaxialcrystal.

Form birefringence may also be obtained for thin films havingmicrostructures therein, wherein the dimension of the microstructuresare smaller than the wavelength of light. Form birefringence incomposite media are also discussed in, e.g., Yeh and Gu, “Optics ofLiquid Crystal Displays”, John Wiley & Sons., Inc. 1999,pp. 381-384.Invarious other embodiments, such composite media that produces formbirefringence may also be employed.

The techniques described above for reducing polarization aberrationscaused by intrinsic birefringence are particularly well suited forproviding wavefront correction of imaging systems used forphotolithography. In addition to the rigorous performance requirementsassociated with this application, photolithography lenses often includea large number of large refractive and other transmissive opticalelements, which together contribute a significant amount of retardance.Wavefront error caused by retardation aberrations can thereforesubstantially limit the resultant resolution obtained by thephotolithographic projection system.

An exemplary projection lens 100, one which contains twenty-one opticalelements A1-A21, eighteen of which are substantially opticallytransmissive to the wavelength of operation, is illustrated in FIG. 1.As discussed above, a similar lens is provided in the tenth embodimentof European Patent Application No. 1 115 019 A2 by D. Shafer et al. Thisoptical system 100 is designed to operate at a central wavelength of157.63 nanometers. The lens 100 provides approximately 5× reduction at anumerical aperture of about 0.80,and has a rectangular image field withdimensions of about 22 mm to 7 mm. The center of the field is offsetfrom the optical axis 106 by about 4.6 mm. The exemplary design employsseventeen lenses A1, A3-A5, A8-A20, one concave mirror A6 and a planarprotecting plate A21. Two other mirrors A2, A7 direct the optical beamalong a separate arm of the system 100. Each of the lenses A1, A 3-A5, A8-A20 as well as the window A21 are formed of calcium fluoride.

Retardation aberrations are calculated for a similar lens having asimilar prescription as disclosed in European Patent Application No. 1115 019 with each of the lens elements comprising [111] cubiccrystalline calcium fluoride having crystal axes substantiallyidentically aligned. Each of these transmissive components A 1, A3-A5,A8-A 20, and A21 is assumed to have an intrinsic birefringence of about−1.1×10⁻⁶ in these baseline computations. The actual value of intrinsicbirefringence may vary. As discussed above, the exemplary system 100includes an optical axis 106. The twenty-one (21) optical elements A1-A21 are aligned along this optical axis 106. An optical beampropagates along the optical axis 106, from the object plane 102 to theimage plane 104 through the elements A1, A3-A5, A8-A20, and A21 in thelens 100. As indicated above, a plurality of mirrors A2, A6, A7 directthe light along an arm of the system 100 that include several refractiveoptical elements A3, A4, A5 through which the beam passes twice. Radiiand some aspheric coefficients were optimized to improve wavefronterrors before intrinsic birefringence was added.

When the effects of intrinsic birefringence associated with the cubiccrystalline lens material are taken into account, system performancedegrades significantly. FIGS. 10A and 10B are graphical illustrationsshowing the net retardance across the system exit pupil for field pointsat the center and edge of the field, respectively, according to anexemplary embodiment in which all transmissive elements A1, A3-A5, A8-A20, and A21, shown in FIG. 1, are identically aligned in threedimensions, with the elements having their [111] crystal axis directionalong the optical axis 106. FIGS. 10A and 10B include the effects ofintrinsic birefringence. FIG. 10A shows the net retardance at variouspositions across the exit pupil for a beam of light originating from apoint in the object field location which is 0 mm away from the opticalaxis 106. FIG. 10B quantifies the net retardance at various locationsacross the exit pupil for a beam of light originating from an off-axispoint in the object field. These two points correspond to center andedge field points, respectively. This edge field point may, for example,map into a point at the edge of the frame of a photolithographyinstrument for processing semiconductor wafers. The peak-to-valleyretardance due to intrinsic birefringence in this exemplary arrangementis approximately 1 wave on-axis and at the extreme field.

In this preceding example, as illustrated in FIGS. 10A-10B, theintrinsic birefringence produces large retardance aberrations andconsequently large wavefront aberrations when each of the substantiallyoptically transmissive elements A1, A3-A5, A8-A20, and A21 comprise[111] cubic crystal calcium fluoride having the respective crystal axesoriented identically. Without compensation, this wavefront aberrationstrongly exceeds the allowable wavefront error for high precisionphotolithography.

The retardance, however, can be reduced by clocking the [111] cubiccrystal elements in a first portion of the optical system 100 andintroducing a uniaxial birefringent element in a second portion of theoptical system. Preferably, this uniaxial birefringent element comprisesa medium having a single birefringence axis and a negativebirefringence. Moreover, the retardance in the two portions preferablycancel, yielding a net reduction in retardance aberration.

FIG. 11 illustrates a similar photolithography system as that presentedin FIG. 1 comprising a plurality of [111] cubic crystal optical elementA1, A3-A5, A8-A21. Additionally, however, a stressed plate A22 havinguniaxial birefringence has been included. This stressed plate A22preferably comprises a rectangular plate stressed along two orthogonalaxes such as depicted in FIG. 6A. These results also apply to a circularplate as well where the stress is uniform throughout the portion ofplate through which the beam passes. Furthermore, the plurality of [111]cubic crystalline optical elements A1, A3-A5, A8-A21 in the lens 100have been appropriately clocked to produce a substantially circularlysymmetric retardance distribution having radially directed localretardance axes. This radial distribution is at least partiallycancelled by the substantially circularly symmetric tangentialdistribution produced by the stressed plate A22.

The dimensions of the exemplary system 100, which is based on the systemin EP 1 115 019 A2,ed in TABLE I. Radii were selected to improvewavefront errors before instrinsic birefringence was added. Several ofthe surfaces are aspheric surfaces and have an aspheric correctionlisted in TABLE II below.

TABLE I Elements Surface Radius Thickness Glass  1 0.000 4.000 A1  2312.337 18.000 CaF₂  3 9682.901 83.000 A2  4 0.000 0.000 REFL  5 0000−414.787 A3  6 −405.53 −22.000 CaF₂  7 −2462.671 −41.117 A4  8 203.797−13.000 CaF₂  9 1424.672 −33.321 A5 10 176.135 −14.000 CaF₂ 11 480.495−16.562 A6 12 241.213 16.562 REFL A5 13 480.495 14.000 CaF₂ 14 176.13533.321 A4 15 1424.672 13.000 CaF₂ 16 203.797 41.117 A3 17 −2461.67122.000 CaF₂ 18 −405.553 409.787 19 0.000 0.000 A7 20 0.000 −70.541 REFL21 0.000 −59.941 A8 22 (aspheric) −190.019 −20.601 CaF₂ 23 −179.904−6.323 A9 24 (aspheric) −210.098 −39.347 CaF₂ 25 473.115 −103.137 A10 26(aspheric) 3696.826 −15.000 CaF₂ 27 −1457.621 −116.884 A11 28 245.073−15.478 CaF₂ 29 (aspheric) 470.016 −119.416 A12 30 −211.145 −46.407 CaF₂31 390.083 −41.600 A13 32 214.849 −15.000 CaF₂ 33 (aspheric) −152.910−22.009 A14 34 −456.248 −36.555 CaF₂ 35 231.784 −1000 A15 36 3335.791−13.249 CaF₂ 37 798.419 −1000 Aperture 38 0.000 −4.033 A16 39 −158.376−46.695 CaF₂ 40 −286.107 −1.000 A17 41 −172.677 −12.000 CaF₂ 42(aspheric) −126.530 −15.768 A18 43 −216.243 −41.405 CaF₂ 44 241.000−1.000 A19 45 −92.147 −44.386 CaF₂ 46 (aspheric) −251.015 −2.210 A20 47−162.887 −24.949 CaF₂ 48 0.000 0.000 A22 49 STRESSED 0.000 −10.701 CaF₂50 0.000 0.000 A23 51 0.000 −11.000 CaF₂ 52 (aspheric) 556.157 0.000 A2153 0.000 −6.000 CaF₂ 54 0.000 −12.000 55 0.000 0.000

TABLE II Element Surface Aspheric Coefficients A8 22 K 0.00000 A0.152508E × 10⁻⁷   B −0.116620 × 10⁻¹² C   0.783384 × 10⁻¹⁶ D 0.159899 ×10⁻¹⁹ E −0.722908 × 10⁻²³ F   0.728881 × 10⁻²⁷ A9 24 K 0.000000 A−0.923147 × 1⁰⁻⁹  B   0.225315 × 10⁻¹² C −0.126393 × 10⁻¹⁵ D   0.158659× 10⁻¹⁹ E −0.351522 × 10⁻²⁴ F −0.111972 × 10⁻²⁷ A10 26 K   0.000000 A0.255822 × 10⁻⁷ B −0.355557 × 10⁻¹² C −0.221879 × 10⁻¹⁶ D   0.325041 ×10⁻²⁰ E −0.820304 × 10⁻²⁴ F   0.797792 × 10⁻²⁸ A11 29 K   0.000000 A0.253064 × ¹⁰⁻⁸ B −0.133794 × 10⁻¹¹ C −0.110469 × 10⁻¹⁶ D −0.376252 ×10⁻²¹ E −0.129137 × 10⁻²⁵ F   0.108061 × 10⁻²⁹ A13 33 K 0.000000 A−0.672468 × 10⁻⁷   B   0.225146 × 10⁻¹¹ C   0.688454 × 10⁻¹⁶ D −0.398582× 10⁻²¹ E   0.875403 × 10⁻²⁵ F −0.559169 × 10⁻²⁹ A17 42 K 0.000000 A −073609 × 10⁻⁷ B −0.219959 × 10⁻¹¹ C −0.714521 × 10⁻¹⁶ D −0.762080 ×10⁻²⁰ E   0.114026 × 10⁻²³ F −0.121463 × 10⁻²⁷ A19 46 K 0.000000 A0.912071 × 10⁻⁷ B −0.297373 × 10⁻¹¹ C −0.119624 × 10⁻¹⁴ D   0.137621 ×10⁻¹⁸ E   0.230309 × 10⁻²² F −0.952224 × 10⁻²⁷ A23 52 K 0.000000 A−0.685740 × 10⁻⁷   B −0.194597 × 10⁻¹⁰ C   0.424640 × 10⁻¹⁴ D −0.112292× 10⁻¹⁶ E   0.533395 × 10⁻²⁰ F −0.149893 × 10⁻²³

As is well known, aspheric surfaces may be defined by followingexpression:Aρ ⁴ +Bρ ⁵ Cρ ⁶ Dρ ⁷ Eρ ⁸ Fρ ⁹where ρ; is the radial dimension. In Table II, K is the conic constant.

To introduce correction for retardance aberration, the last lens elementA 20 has been split into a plane parallel plate A22, which is stressed,and two lens A20 and A23. The window A21 is adjacent the added lens A23.The plane parallel plate A21 may comprise [111] cubic crystal calciumfluoride with the [111] axis substantially parallel to the optical axis106, and the two lenses A20 and A 23 preferably comprise [111] cubiccrystal calcium fluoride with the [111] crystal axis substantiallyparallel to the optical axis 106. The stress applied to the planeparallel plate A22 produces a uniaxial birefringence of about −2×10−6along, i.e., parallel to, the optical axis 106. Such a component A22,therefore behaves as a negative uniaxial crystal having a single crystalaxis aligned with the optical axis.

In addition, the substantially [111] cubic crystalline optical elementsA 1, A3-A5, A8-A21, and A23, are clocked as described above, to providea circularly symmetric radial retardance distribution. The direction andamount of axial rotation is selected to yield retardance substantiallyequal to but opposite the retardance introduced by the uniaxialbirefringent optical element, i.e. the stressed plate A22, which has aretardance like that of a uniaxial crystal with negative birefringence.These elements A1, A3-A5, A8-A21, and A23 are considered the firstportion of the optical system 100. Exemplary clocking values for thissystem 100 are shown in TABLE III. For [111] optical elements orientedwith their [111] crystal axis along optical axis 106, preferably theclocking of each element is given relative to an orientation thatproduces peak retardance lobes 60, 180,and 300 degrees in the pupil. Itshould be understood that such is exemplary only and the relativeclocking of the elements may be described with respect to any of variousarbitrary reference locations. Positive rotations are right handed aboutthe local +Z axis at the lens element.

TABLE III Element Surface Clocking (degrees)  1  0 A1  2  36  3  0 A2  4 0 (reflector)  5  0 A3  6  7  7  0 A4  8 181  9  0 A5 10 246 11  0 A612  0 (reflector) A5 13 246 14  0 A4 15 181 16  0 A3 17  7 18  0 19  0A7 20  0 (reflector) 21  0 A8 22 (aspheric) 268 23  0 A9 24 (aspheric)239 25  0 A10 26 (aspheric) 359 27  0 A11 28  22 29 (aspheric)  0 A12 30 20 31  0 A13 32 193 33 (aspheric)  0 A14 34  66 35  0 A15 36 245 37  0A.S. 38  0 A16 39 303 40  0 A17 41 332 42 (aspheric)  0 A18 43 333 44  0A19 45  32 46 (aspheric)  0 A20 47 434 48  0 A22 49 STRESSED  43 50  0A23 51 333 52 (aspheric)  0 A21 53 168 54  0 55  0

The stressed plate A 22 corresponds to the second portion of the opticalsystem 100, two portions preferably substantially offsetting each otherso as to reduce net retardance aberrations. FIG. 12 is a graphicalrepresentation that depicts the net retardance across the system exitpupil at an extreme edge field point due to intrinsic birefringence ofall elements A1-A23, including the stressed plate. The extreme edgepoint in this example is about 55 mm on the x-axis and 40 mm on they-axis (x=−55 mm; y=40 mm) As shown, the net retardance has beensignificantly reduced compared with the retardance for all [111]elements without the stressed plate A22, which is shown in FIG. 1, andwithout the appropriate clocking.

The RMS and maximum retardance over the exit pupil are listed in TABLEIV below for nine field positions. The results for field nine aregraphically FIG. 12. The intrinsic birefringence of about −1. 1×10⁻⁶ wasassumed for the [111] cubic crystal optical elements. The RMS retardanceranging from 0.0094 to 0.0146 waves at λ₀=157 nm is shown. A greaterthan about 10×reduction in retardance aberration is achieved in thisexample. The numerical aperture of this system 100 is about 0.8.In thisembodiment, the variation in net retardance after compensation with thenegative uniaxial structure is minimal. However, if there weresignificant variation across the field, then one or more additionaluniaxial structures could be placed elsewhere in the lens to reduce orminimize the variation of retardance aberrations over the field.

TABLE IV Field Retardance (waves) Number X (mm) Y (mm) Maximum RMS 1 023 0.0555 0.0097 2 39 6 0.0466 0.0094 3 55 6 0.0721 0.0126 4 39 400.0651 0.0133 5 55 40 0.0844 0.0142 6 −39 6 0.0564 0.0104 7 −55 6 0.07600.0136 8 −39 40 0.0631 0.0120 9 −55 40 0.0847 0.0146

As illustrated, the net retardance has been significantly reducedcompared with the retardance for the all [111] element system 100without clocking and without the stressed plate A22, which are shown inFIGS. 10A and 10B. Thus, substantial retardance correction for a system100 comprising all [111] optical elements is possible by appropriatelyclocking the [111] elements and using one or more uniaxial birefringentelements A22 that have a retardance distribution conjugate to theretardance of the clocked [111] elements. In particular, the systemretardance associated with this catadioptric optical system 100 issignificantly reduced to levels acceptable for high numerical aperturelithography.

The retardance can also be reduced by clocking the cubic crystalelements in a first portion of the optical system 100 and introducingone or more form birefringent optical element having a singlebirefringence axis into a second portion of the optical system. Theretardance in the two portions preferably cancels, yielding a netreduction in retardance aberration.

FIG. 13 illustrates a similar photolithography system 100 as thatpresented in FIG. 1 with the addition of a thin film layer X 22 having auniaxial birefringence formed on the surface (51) of one of the opticalelements A23. In one example, this thin film layer X 22 is about 5microns thick although the dimensions of the thin film layer X22 shouldnot be so limited. (The size of this thin film layer X22 is exaggeratedfor clarity in this drawing.) The thin film X22 preferably comprisesalternating layers of material having different indices of refractionsuch as depicted in FIG. 8. More specifically, this multilayer film X22is preferably substantially optically transmissive at the wavelength ofoperation and provides form birefringence as discussed above. Inaddition, the plurality of [111] cubic crystalline calcium fluorideoptical elements A1, A3-A5, A8-A 21, and A23 have been appropriatelyclocked to produce a substantially circularly symmetric retardancedistribution having radially directed retardance axes. This radialdistribution is at partially canceled by the substantially circularlysymmetric tangential distribution of the form birefringent multilayer.

The dimensions of the exemplary system 100, which is based on the systemin EP 1 115 019 A2,are listed in TABLE V. Several of the surfaces areaspheric surfaces, and have the aspheric correction listed in TABLE IIabove. The optically transmissive lens elements A 1, A3-A5, and A8-A20as well as the window A21 were assumed to be formed from [111] cubiccrystal calcium fluoride with respective [111] crystal axes parallel tothe optical axis 106. 5

TABLE V Element Surface Radius Thickness Glass  1 0.000 4.000 A1  2312.337 18.000 CaF₂  3 9682.901 83.000 A2  4 0.000 0.000 REFL  5 0.000−414.787 A3  6 −405.553 −22.000 CaF₂  7 −2462.671 −41.117 A4  8 203.797−13.000 CaF₂  9 1424.672 −33.321 A5 10 176.135 −14.000 CaF₂ 11 480.495−16.562 A6 12 241.213 16.562 REFL A5 13 480.495 14.000 CaF₂ 14 176.13533.321 A4 15 1424.672 13.000 CaF₂ 16 203.797 41.117 A3 17 −2462.67122.000 CaF₂ 18 −405.553 409.787 19 0.000 0.000 A7 20 0.000 −70.541 REFL21 0.000 −59.941 A8 22 (aspheric) −190.019 −20.601 CaF₂ 23 −179.904−6.323 A9 24 (aspheric) −210.098 −39.347 CaF₂ 25 473.115 −103.837 A10 26(aspheric) 3696.826 −15.000 CaF₂ 27 −1457.621 −116.884 A11 28 2415.073−15.478 29 (aspheric) 470.016 −119.416 A12 30 −211.145 −46.407 CaF₂ 31390.083 −41.600 A13 32 214.849 −15.000 CaF₂ 33 (aspheric) −152.910−22.009 A14 34 −456.248 −36.555 CaF₂ 35 231.784 −1.000 A15 36 3335.791−13.249 CaF₂ 37 798.419 −1.000 Aperture 38 0.000 −4.033 A16 39 −158.376−46.695 CaF₂ 40 −386-107 −1.000 A17 41 −172.677 −12.000 CaF₂ 42(aspheric) −126.530 −15.768 A18 43 −216.243 −41.405 CaF₂ 44 241.000−1.000 A19 45 −92.147 −44.386 CaF₂ 46 (aspheric) −251.015 −2.210 A20 47−162.887 −35.645 CaF₂ 48q 0.000 0.000 X22 49 FILM 0.000 −0.005 CaF₂ 500.000 0.000 A23 51 0.000 −11.000 CaF₂ 52 (aspheric) 556.157 0.000 A21 530.000 −6.000 CaF₂ 54 0.000 −12.000 55 0.000 0.000

To introduce correction for retardance aberration, the last lens elementA 20 is split into two lens A20 and A 23. A form birefringent coatingX22 has been included between the two lenses A20, A23. This formbirefringent coating X22 may, for example, be formed on the surface (51)of the added lens A 23. The window A21 is adjacent the additional lensA23. Both lenses A20 and A23 were assumed to be [111] cubic crystalcalcium fluoride. Calculations are based on a form birefringent coating200 that comprises alternating layers of relatively high (n₁) and low(n₂) indices of refraction of 1.8 and 1.47,respectively. As discussedabove, for example, the high index layers may comprise LaF₃ or GdF₃, andthe low index layers may comprise AlF₃ or MgF₂. Other materials may beused as well. The form birefringent coating X22 was assumed to be 5.0micrometers thick and to yield a uniaxial birefringence of about 0.04.Such a structure X22 behaves as a negative uniaxial crystal having abirefringent or crystal axis normal to the planar surface (51) andparallel to the optical axis 106.

In addition, the substantially [111] cubic crystalline optical elementsA 1, A3-A5, A8-A21, and A23 are clocked, as described above, to providea circularly symmetric radially directed retardance distribution. Thedirection and amount of axial rotation is selected to produce aretardance pattern substantially equal to but opposite the retardancedistribution introduced by the uniaxial birefringent optical element,i.e. the form birefringent coating X22. As discussed above, the formbirefringent coating X22 has a birefringence similar to that of auniaxial crystal with negative birefringence. These [111] cubic crystaloptical elements A1, A 3-A5, A8-A21, and A 23 are considered the firstportion of the optical system 100 which balanced or matched by theretardance introduced by the form birefringent coating X22. Exemplaryclocking values for this system 100 are shown in TABLE VI Positiverotations are right handed about the local +Z axis at the lens element.6

TABLE III Element Surface Clocking (degrees)  1  0 A1  2 334  3  0 A2  4 0 (reflector)  5  0 A3  6  79  7  0 A4  8 135  9  0 A5 10 197 11  0 A612  0 (reflector) A5 13 197 14  0 A4 15 135 16  0 A3 17  79 18  0 19  0A7 20  0 (reflector) 21  0 A8 22 (aspheric)  72 23  0 A9 24 (aspheric)178 25  0 A10 26 (aspheric) 181 27  0 A11 28 181 29 (aspheric)  0 A12 30173 31  0 A13 32  2 33 (aspheric)  0 A14 34 123 35  0 A15 36 203 37  0Aperture 38  0 A16 39  37 40  0 A17 41 234 42 (aspheric)  0 A18 43 34044  0 A19 45 360 46 (aspheric)  0 A20 47  58 48  0 X22 49 FILM  0 50  0A23 51 272 52 (aspheric)  0 A21 53  77 54  0 55  0

The form birefringent coating X22 corresponds to the second portion ofthe optical system, the two portions preferably substantially offsettingeach other so as to substantially reduce net retardance aberrations.FIG. 14 is a graphical representation that depicts the net retardanceacross the system exit pupil at an extreme edge field point due tointrinsic birefringence of all elements A1-A23, including the formbirefringent coating X22. As shown, the net retardance has beensignificantly reduced compared with the retardance for the comparablesystem 100 comprising all [111] elements without the form birefringentcoating X22 which is shown in FIG. 1. The resultant retardance foroff-axis points for this uncorrected system 100 is present in FIG. 10Bas discussed above.

The RMS and maximum retardance over the exit pupil are listed in TABLEVII below for nine field positions. The results from the ninth fieldpoint are graphically illustrated in FIG. 14. The RMS retardance rangingfrom 0.0118 to 0.0173 waves at λ₀=157 nm is shown. This residualretardance is largely a fourth order variation. Accordingly, greaterthan about 10×reduction in retardance aberration is achieved in thisexample. The numerical aperture of this system 100 is about0.8.Intrinsic birefringence of about −1.1×10⁻⁶ been assumed for the[111] cubic crystal optical elements.

TABLE VII Field Retardance (waves) Number X (mm) Y (mm) Maximum RMS 1 023 0.0607 0.0118 2 39 6 0.0704 0.0127 3 55 6 0.0813 0.0146 4 39 400.0769 0.0142 5 55 40 0.0844 0.0142 6 −39 6 0.0682 0.0123 7 −55 6 0.08910.0150 8 −39 40 0.0739 0.0145 9 −55 40 0.0910 0.0173

In various preferred embodiments, an impedance matching layer 300 suchas shown in FIG. 15 is included between the form birefringencemultilayer 200 and the substrate 202, i.e., the optical element, uponwhich the coating is formed. This impedance matching layer 300 maycomprise a plurality of layers 304, 306 of material formed on thesurface 201 of the optical element 202. This plurality of layers 304,306 may comprise similar materials as the layers 204, 206 in the formbirefringent multilayer structure 200. These impedance matching layers304, 306 preferably correspond to high and low index layers comprisingmaterials having respective high and low indices of refraction n₁, n₂.Examples of high index materials may include LaF₃ and GdF₃ having anindex of refraction of 1.8 while exemplary low index materials mayinclude AlF₃ and MgF₂ having an index of refraction of about 1.47.Othermaterials may be employed in various other embodiments, and thesematerials need not be the same as those 204, 206 in the formbirefringent multilayer structure 200. Use of similar materials,however, may simply fabrication. In various embodiments, the thicknessof the layers 304, 306 may be adjusted to provide the desired effectiveindex of refraction of the aggregate structure 300 or the high and lowindex material may be deposited simultaneously to form a compositematerial with a refractive index between that of the two base materials.

Without impedance matching, index mismatch between the calcium fluorideoptical element 202 and the effective index of the form birefringencemultilayer 200 will cause reflection. Accordingly, a portion of thelight propagating through the form birefringence multilayer 200 isreflected from the surface 201 of the calcium fluoride optical element202 as a result of Fresnel reflection.

Additional Fresnel reflection is produced at the “air”/form birefringentcoating interface 310. A portion of the light incident on the formbirefringent coating 200 is reflected as a result of the index mismatchbetween the “air” (or other ambient medium) and the form birefringentcoating. Conversely, light propagating through optical element 202 andthe form birefringence coating 200 into the “air” will be partiallyreflected back into the form birefringent coating.

Together, the two reflective interfaces, i.e., the “air”/formbirefringent coating interface 310 and the surface 201 of the calciumfluoride optical element 202, create a weak optical cavity. The effectsof this optical cavity are illustrated in FIG. 16A which depicts thetransmission of light through the form birefringent coating 200 withoutthe impedance matching layer 300. Curves 312 and 314 represent s and ppolarization, and curve 316 corresponds to an average between of thesetwo polarizations. The curve 312, 314, 316 plot the variation oftransmittance with angle of incidence. Ripple is observed in the threecurves 312, 314, 316 as both reflectance and cavity resonance varieswith angle of propagation of light incident on the reflective interfaces316, 201 and through the weak optical cavity.

The impedance matching layer 300 between the form birefringent layers200 and the calcium fluoride optical element 202 reduces the indexmismatch at the surface 201 and preferably substantially weakens thecavity effects. FIG. 16B depicts transmission of light through the formbirefringent coating 200 and the calcium fluoride optical element 202with the impedance matching layer 300 therebetween. The formbirefringent coating 200 in this example is the same structure used inconnection with the example associated with FIG. 16A. Curves 322 and 324represents and p polarization, and curve 326 corresponds to an averagebetween of these two polarizations. These curves 322, 324, 326 also plotthe variation of transmission with angle of incidence. Ripple issubstantially lessened as reflectance at the surface 201 of the calciumfluoride element 202 is reduced and the cavity affects diminish.

For reference, FIG. 16C shows the transmission of light through a barecalcium fluoride optical element 202. Neither the form birefringentmultilayer 200 nor the impedance matching layer 300 are included in thisexample. Accordingly, the cavity affects such as ripple are removed. Inthis plot, curves 332 and 334 correspond to s and p polarization, andcurve 336 represents an average between of these two polarizations.

Adding the impedance matching structure 300 between the formbirefringent coating 200 and the calcium fluoride substrate 202 also mayimprove the variation in birefringence with angle of incidence. Todemonstrate this effect, the phase delay between orthogonal polarizationstates is computed for different angles of incidence. FIG. 17A depictsthis relationship for a form birefringent coating 200 on a calciumfluoride optical element 202 without an impedance matching layer 300.Irregular fluctuation, i.e., ripples, are observable in this plot.

The inclusion of an impedance matching layer 300 substantially removesthis ripple as shown in FIG. 17B, which plots the phase shift betweenthe orthogonal polarizations for light incident on the structure at avariety of angles. The curve is substantially smoother than that shownin FIG. 17A.

In the examples above corresponding to FIGS. 16A-16C and 17A-17B, thewavelength of light was 157.0 nanometers and ambient was air. The formbirefringent coatings 200 comprise one hundred and three (103) pairs ofhigh and low index materials with indices of 1.8 and 1.47,respectively.These layers each have an optical thickness (index×thickness) of about0.49 and 0.4 quarter-waves (i.e., n×t=0.49 λ/4 and n×t=0.4 λ/4) for thehigh and low index materials, respectively. The impedance matching layer300 comprises two (2) pairs of high and low index materials with indicesof 1.8 and 1.47,respectively. These high and low index layers haveoptical thicknesses of about 0.205 and 0.295 quarter waves (i.e.,n×t=0.205 λ/4 and n×t=0.295 λ/4), respectively. Preferably, thesethicknesses were selected to provide an effective index of refractionfor the impedance matching layer 300 having a value approximately equalto the square root of the product of the index of the calcium fluoridesubstrate and the effective index of the form birefringent coating, tothereby reduce the index mismatch. Other intermediate values between theeffective index of the form birefringent coating and the index ofcalcium fluoride are possible. This impedance matching coating may bereferred to as an anti-reflection coating as it reduces reflection. Thisexample impedance matching coating is, however, meant to be exemplaryand not limiting. Those skilled in the art of coating design willrecognize that many other types and variation of impedance matchingcoatings are possible.

Accordingly, impedance matching layer 300 between the form birefringentcoating 200 and the calcium fluoride substrate 202 may significantlyreduce index mismatch and cavity effects created by these indexmismatches. Transmission and birefringence comparable with that of anuncoated, i.e., bare calcium fluoride substrate are possible.

An anti-reflection coating 311 may also be included on the formbirefringent coating 300 to reduce reflection at the “air”(ambient)/form birefringent coating intereface 310. This anti-reflection(AR) coating 311 may be a conventional AR coating well known in the artsuch as for example a quarter-wave stack. Preferably, this AR coating311 comprises material the same as or compatible with those in the formbirefringent layer 200. This AR coating 311, may for example, comprisemultiple layers of high and low index materials with indices of 1.8 and1.47,respectively, such as LaF₃ and GdF₃, and AlF₃ and MgF₂. The typeand quantity (e.g., layer thickness) of material is not to be limited tothe examples described herein and other anti-reflection coatingtechnologies including those yet to be devised are also consideredpossible.

Like the impedance matching layer 300, the AR coating 311 may reduce thereflections at the interface 310 so as to decrease the cavity affectsand also reduce transmission losses. Other techniques may also beemployed to remove cavity affects and improve transmission as well. Forexample, the form birefringence coating 200 may be formed on a buriedlayer imbedded between two calcium fluoride elements 202. A pair ofimpedance matching multilayer structures 300, one on each side of theform birefringent coating, may be used to reduce index mismatch betweenthe calcium fluoride material and the form birefringent multilayers 200.

Employing form birefringence to provide a birefringence characteristicakin to a negative uniaxial crystal offers several advantages over useof a stress plate 180, 190. In some respects, a form birefringent mediumis simpler to implement. A mechanical structure physically attached tothe stressed optical element need not be used to apply compressive ortensile stresses. The applied stress may, in some cases, be temperaturedependent for example when a tight metal band surrounds the perimeter ofthe optical element. Such a band may expand and contract with changes intemperature, causing the applied force and resultant birefringence tofluctuate. In other case, the stress-induced birefringent element may beeasier to fabricate than certain form birefringence material structures.

Application of the various techniques and designs described herein arenot to be limited only to those lens 100 discussed above but may beapplied broadly to a wide range of optical systems. For example,although the lens 100 depicted in FIGS. 11 and 13 included twenty-threeoptical elements A1-A 23, other embodiments may comprise more or lessoptical elements which may be reflective, diffractive, and/orrefractive. Similarly, the optical elements may have spherical oraspheric surfaces, may be powered or unpowered, may be off-axis or onaxis. Other optically transmissive elements may include diffractive andholographic optical elements, filters, retro-reflectors, beamsplitters,to name a few. The techniques and designs described above are usefulboth for imaging and non-imaging systems such as for examplephotolithographic imaging lenses as well as projection and condenserlenses but should not be limited to these applications alone.

Other compensation techniques may be applied to reduce retardance. Oneof these techniques includes, for example, adding [100] optical elementsthat are appropriately rotated with respect to the optical axis toprovide compensation. Other methods employ a polarization rotator toprovide compensation between polarization aberrations introduced byvarious parts of the optical system 100. Still other methods of reducingretardance and other polarization aberrations may be used in conjunctionwith the techniques and designs describe herein.

Also, in other embodiments, one or more of the optical elements A 1,A3-A5, A8-A21, and A 23 may comprise crystalline material other thancubic crystals as well as non-crystalline materials such as amorphousglasses. Fused silica is an example of such a non-crystalline materialthat is substantially optically transmissive to UV wavelengths such as248 nm and 193.3 nm and is therefore compatible with such UVapplications. In the case where at least some of the elements A1, A3-A5,A8-A 21, A23 are crystalline, they do not need to all be the samecrystal orientation. For example, various combinations of cubic crystaloptical element having a [111], [100], and/or [110] crystal directionmay be suitable employed.

In various of the examples described above with respect to FIGS. 11 and13, all these transmissive optical elements A1, A 3-A5, A8-A21, and A23,are [111] cubic crystalline elements. The [111] crystal latticedirection for each element A1, A 3-A5, A8-A21, and A 23, is along thesystem optical axis 106. [0159] Choosing as many cubic crystallineelements with their respective [111] crystal lattice directions alongthe system optical axis is particularly advantageous for construction ofoptical systems 100. As discussed above, high purity cubic crystals,such as CaF₂ crystals for VUV optical lithography systems, naturallycleave along the (111) plane, and high optical quality single crystalsare more easily grown along the [111] direction. As a result, lensblanks for construction of [111] optical elements are typically lessexpensive and more readily available than lens blanks oriented alongother lattice directions. Furthermore, the stress optic coefficient islower along the [111] direction than along the [100] or [110]directions, reducing image degradation resulting from mount-inducedstress. Accordingly, an example of this preferred arrangement ispresented, in which all powered cubic crystalline elements comprise[111] refractive optical elements oriented with their respective [111]crystal axes along the optical axis.

Alternate embodiments, however, may include optical componentscomprising other cubic crystal material having their crystal axesoriented differently. The lens may for example include one or more [100]and/or [110] optical elements with the respective [100] and [110]lattice directions substantially parallel to the optical axis 106.Preferably, however, the majority or more preferably a substantialmajority of the cubic crystal optical elements through which the beampasses in the optical system comprise [111] optical elements. Forexample, 70, 80, 90,percent or more of the cubic crystalline opticalelements in the path of the beam in the optical system 100 preferablycomprise [111] cubic crystal optics. These percentages may apply to justthe cubic crystal lens elements or may include both lens elements aswell as other optical elements, such as, e.g., windows and plates.Alternatively, the percentage, by weight, of [111] cubic crystal of allthe cubic crystal material in the optical path of the lens 100 ispreferably more than 50%, more preferably at least about 80% and mostpreferably 90% or more. This percentage may include only poweredrefractive optical elements as well as powered and non-powered opticalelements such as windows and plates, etc. For example, 90% of net weightof the cubic crystal lens 100 may comprise cubic crystal having a [111]axis oriented along the optic axis 106. In another example, 80% of thenet weight of the cubic crystal optics, including the protective windowA21, may be [111] cubic crystal, with the [111] axis parallel to theoptic axis. The cost of materials for such a system 100 is significantlyreduced in comparison with optical systems that employ more [110] or[100] crystal material. The use of a uniaxial birefringent medium andappropriate clocking in reducing the retardance aberration enables sucha large percentage by weight of [111] crystal material to be usedwithout unduly degrading the optical performance of the system 100. Inother embodiments, some of the lens elements A 1, A 3-A5, A8-A23 orother optical elements may be formed of non-cubic crystalline materialor additional lens and/or optical elements formed of non-cubiccrystalline material may be used. Various suitable non-cubic crystallinematerials such as dry fused silica may offer other lower costalternatives.

Some of the preceding examples are based on a lens prescriptionpublished in the prior art. These examples are intended to be exemplaryonly and the principles applied with reference to these examples can beextended to any of various other lens designs. Application of techniquesdescribed above for reducing retardance aberration are of particularinterest for high numerical aperture optical systems forphotolithography at an exposure wavelength near 157 nm, such as thatproduced by an F₂ excimer laser. It should be understood, however, thatthese principles and techniques apply equally to both high and lownumerical aperture systems and systems operating at other wavelengths.For example, substantial reduction in the net retardance or retardanceaberrations may be reduced for high performance lenses 100 having anumerical apertures about 0.6, 0.7, 0.8, 0.9 or more. Corrections oflower numerical aperture (larger F-number) systems is also possible andis in many cases is less difficult. As discussed above, for instance,the retardance pattern for the optical elements A1, A3-A5, A8-A 21, A23may be more uniform, more circularly symmetric and more radial for lowernumerical apertures.

Furthermore to estimate the effects of intrinsic birefringence in highnumerical aperture lenses designed for a central wavelength of 157 nm,in which the refractive elements are primarily constructed from calciumfluoride, each element is assumed to have a peak intrinsic birefringenceof (n_(e)−n_(o))=−1.1×10⁻⁶, which is roughly equivalent to the measuredpeak intrinsic birefringence in calcium fluoride at a wavelength of 157nm. In other embodiments, however, one or more of the optical elementsmay be constructed from other materials such as barium fluoride, lithiumfluoride, strontium fluoride, and fused silica. In addition, opticalelements comprising material exhibiting positive birefringence can beincluded to compensate for the effects of optical elements comprisingmaterial exhibiting negative birefringence.

The method for compensation for intrinsic birefringence in similar highnumerical aperture lenses designed for 157 nm may also be demonstratedusing known exemplary lens descriptions designed for a centralwavelength of 193 nm as starting points. The change in centralwavelength may result in a change in refractive index of the refractivecomponents and may warrant the use of fluoride materials such as calciumfluoride, but the types of elements used and distributions of ray anglesfor a given numerical aperture are similar enough to allow a lensdesigned for a central wavelength of 193 nm to be used to demonstratethe innovative techniques for mitigating the effects of intrinsicbirefringence in high numerical aperture lenses, at a central wavelengthof 157 nm. The design techniques presented above, however, may beemployed for reducing polarization aberration in optical systemsoperating at other wavelengths.

The preceding examples are intended to be illustrative, not restrictive.Furthermore, it is intended that the various exemplary techniques forcountering the effects of intrinsic birefringence, including retardanceaberrations and wavefront aberrations produced by variations in averageindex of refraction, may also be applied to the other embodiments. Moregenerally, these basic principles used to compensate for polarizationaberrations such as retardation can be extended to at least partiallycorrect for these effects in various other optical systems. Theprinciples apply both to refractive and catadioptric lens systems aswell as other systems containing substantially optically transmissivematerial that imparts polarization aberrations on a beam propagatingtherethrough. In other optical systems, the optical features of theoptical components may vary. For example, the individual thicknesses,radii of curvature, aspheric coefficients, and ray angles may differsignificantly from component to component.

These principles may be used when designing new optical systems or toimprove a known lens prescription. In some of the examples above, thecorrected optical system is based on a given lens prescription, whichmay be maintained and the effects of intrinsic birefringence compensatedfor, using the techniques described above. Alternatively, retardationmay be reduced by splitting of one or more lens elements of the givenprescription, into two or more sub-elements. The location of the buriedsurface, its curvature and the thicknesses of the respectivesub-elements are degrees of freedom that may be adjusted to reduceaberration or provide other performance attributes. For example, theoptical power may be substantially evenly split into the sub-elements,which may or may not have same center thickness. The techniques anddesigns described above, however, may be advantageously applied tovarious other new lens prescriptions being designed.

Ray tracing software may be used to generate or revise the lensprescription including positioning of the individual lens elements, aswell as thicknesses, radii of curvature, aspheric coefficients, materialproperties, and the like. In one embodiment, the RMS retardance may becomputed over a pupil grid at each field point and used as the meritfunction for a damped least squares optimization using the commerciallyavailable ray tracing software, CODE V®, for example. A computer may beused to optimize the orientation and clocking of each of the elements inthe system and the thickness of the uniaxial birefringent medium. Thethicknesses of the components, the spacings between the components, andthe radii of curvature and aspheric coefficients of the lens elements,may similarly be optimized to balance aberrations and reduce retardanceacross the field. One or more birefringent elements, wave plates, orcombinations thereof, may additionally be used to correct for residualretardance variation and constant residual retardance. Phaseaberrations, such as astigmatism, trefoil aberration, and quadrafoilaberration, introduced by the average index variations in [110], [111],and [100] elements, respectively, may be compensated using one or moresurfaces with radii of curvature that vary as 2θ, 3θ,and4θ,respectively.

When cubic crystalline materials like calcium fluoride are used, asubstantial portion of these crystal elements preferably comprise lesserexpensive [111] cubic crystal with the [111] crystal lattice directionparallel to the optical axis 106. Although [100] and [110] elementsappropriately clocked can be added to compensate for the retardanceintroduced by [111] elements, the cost of these [100] and [110] elementsis higher. The techniques described above advantageously permit theretardance of the [111] elements to be compensated for by other thelesser expensive [111] elements. Accordingly, the fraction of cubiccrystalline elements that comprise [111] crystal with the [111] crystallattice direction along the optical axis is preferably large, i.e. , atleast 70-90%, by weight. Although the uniaxial birefringent medium maybe formed from various materials, it may comprise cubic crystal, such as[110], [100], or [111] cubic crystal elements. In some embodiments wherethe uniaxial birefringent element comprises cubic crystal, preferably itcomprises mostly [111] cubic crystal, most preferably, all [111] cubiccrystalline material. As discussed above, having many of the cubiccrystal elements comprise [111] material reduced the cost of the optics.Most preferably, a majority of the transmissive optical elements have anoptical axis generally aligned with the [111] crystal lattice direction.In one preferred embodiment, substantially all the opticallytransmissive cubic crystal elements comprise this [111] crystal.

As mentioned above, the various exemplary cubic crystalline opticalsystems and methods for forming aberration-free patterns onsemiconductor substrates are particularly advantageous as feature sizesbecome increasingly smaller and approach the half or less than halfwavelength of the light used to produce the patterns. Such techniquesfind particular advantage in high numerical aperture (NA) lens systemsbut the various aspects of these methods and innovations findapplication in optical systems having both relatively high andrelatively low numerical apertures.

Although described in conjunction with photolithography tools used topattern substrates in the semiconductor industry, the techniques anddesigns discussed above will find use in a wide variety of applications,both imaging and non-imaging, in infrared, visible, and ultraviolet.Optical systems used for medical, military, scientific, manufacturing,communication, and other-applications are considered possible candidatesfor benefiting from the innovations described herein.

Although described above in connection with particular embodiments ofthe present invention, it should be understood the descriptions of theembodiments are illustrative of the invention and are not intended to belimiting. Accordingly, various modifications and applications may occurto those skilled in the art without departing from the true spirit andscope of the invention. The scope of the invention is not to be limitedto the preferred embodiment described herein, rather, the scope of theinvention should be determined by reference to the following claims,along with the full scope of equivalents to which those claims arelegally entitled.

1. An optical method comprising: propagating a beam of light havingfirst and second orthogonal polarization components through first opticscomprising a plurality of optical elements disposed along an opticalaxis, said first optics having radial and tangential eigenpolarizationstates that form a circularly symmetric pattern around said opticalaxis, said radial and tangential eigenpolarization states being phaseddelayed with respect to each other so as to introduce phase delaybetween said first and second orthogonal polarization components in saidbeam of light; and substantially reducing said phase delay between saidfirst and second orthogonal polarization components in said beam oflight by propagating said light through second optics disposed alongsaid optical axis, said second optics having radial and tangentialeigenpolarization states that form a circularly symmetric pattern aroundsaid optical axis, said radial and tangential eigenpolarization statesin said second optics being phased delayed with respect to each otheropposite said phase delay between said radial and tangentialeigenpolarization states of said first optics.
 2. The method of claim 1,wherein the plurality of optical elements of the first optics comprisesa plurality of cubic crystal optical elements clocked such that saidradial and tangential eigenpolarization states form a circularlysymmetric pattern around the optical axis passing through said pluralityof cubic crystal elements.
 3. The method of claim 1, comprisingpropagating said light through an optical element of said second optics,the optical element having a stress-induced uniaxial birefringence usedto reduce said phase delay.
 4. The method of claim 1, comprisingpropagating said light through an optical element of said second optics,the optical element having a stress-induced uniaxial birefringence dueto a stress imposed on the perimeter of front and rear surfaces of theoptical element, said light propagating through the optical element isincident on said front face and exits said rear face.
 5. The method ofclaim 1, comprising propagating said light through an optical element ofsaid second optics, the optical element comprising a [111] cubic crystaloptical element having a stress-induced uniaxial birefringence.
 6. Themethod of claim 1, comprising propagating said light through an opticalelement of said second optics, the optical element having a formbirefringence media.
 7. The method of claim 1, comprising propagatingsaid light through an optical element of said second optics, the opticalelement having a uniaxial birefringent media that includes at least onemultilayer form birefringence film comprising multiple layers eachhaving a thickness of less than a wavelength.
 8. The method of claim 1,comprising propagating said light through an optical element of saidsecond optics, the optical element having a uniaxial birefringent mediathat includes a composite form birefringent structure comprising aplurality of microstructures imbedded in a material.
 9. The method ofclaim 1, comprising propagating said light through a cubic crystaloptical element of said first optics, the cubic crystal optical elementcomprising [111] cubic crystal.
 10. The method of claim 1, comprisingpropagating said light through a cubic crystal optical element of saidfirst optics, the cubic crystal optical element comprising [100] cubiccrystal.
 11. The method of claim 1, wherein said first and second opticscorresponds to a numerical aperture of at least about 0.7.
 12. Themethod of claim 1, wherein said light has a wavelength less than orequal to about 193 nm.
 13. The method of claim 1, wherein said first andsecond optics form a catadioptric system including at least onereflective surface.
 14. The method of claim 1, comprising propagatingsaid light through a fused silica optical element of said first optics,of said second optics, or both.
 15. The method of claim 14, wherein saidfused silica optical element is a powered lens element having a surfacewith asymmetric variation in curvature configured to reduce wavefrontaberration.
 16. The method of claim 1, comprising propagating said lightthrough a cubic crystal optical element of said first optics, of saidsecond optics, or both, the cubic crystal optical element having anaspheric surface configured to reduce wavefront aberration.